Linear Function Research Articles

The delineation of management zones using soil quality indices for the cultivation of irrigated rice (Oryza sativa L.) in Huila, Colombia

Conventional intensive farming systems can result in degraded soil. It is therefore important to monitor this effect periodically by delineating management zones (MZ) based on soil quality indices (SQI) in order to maintain and improve the soil characteristics in a precision farming environment and obtain homogeneous rice yields. The aim of this study was to determine and spatialise SQI and delineate MZ for cultivating flooded rice in an area of Fluvisols in Huila, Colombia. Forty-one georeferenced soil samples were collected from the 0 to 20 cm layer, and the physical, chemical and biological attributes of the soil were analysed to calculate the Integrated Quality Index (IQI) and the Nemoro Quality Index (NQI) using linear scoring functions. Geostatistical tools were then used to fit semivariogram models of the SQI, and interpolated using ordinary kriging to map the MZ using the QGIS software. The IQI and NQI showed a moderate spatial correlation, which allowed three distinct MZ to be identified and delineated. Attributes, such as bulk density (Bd), total porosity (TP), soil respiration (SR), available water (AW) and soil organic matter (SOM) were significant and can be used as a guide by farmers for restoring the quality of the soil in rice production. The method proved to be effective, and provided an information base to be used in the local management of areas of rice cultivation in the study region.

Robust α-exponential estimate for polytopic uncertain positive discrete-time systems with bounded time-varying delay

In this paper, the problem of finding a robust α-exponential estimate for a class of perturbed positive discrete-time time-delay systems with polytopic uncertainties will be addressed. By proposing a linear parameter-dependent Lyapunov function, a condition for the existence of robust α-exponential estimates will be introduced. Some optimisation techniques are also incorporated to obtain a more accurate estimate. In particular, a procedure to reformulate a class of fractional programming problems into a linear programming problem which can be solved efficiently. A numerical example is presented to demonstrate the effectiveness of the proposed method.

The study of the calculation method of the triboelectric rate of particles and surface materials at different collision velocities

In this paper, a triboelectric rate calculation model based on the relative collision velocity between the material and the particle is put forward. The model demonstrates distinct trends of the triboelectrification rate's increase with velocity, ranging from a 9/5 power to a linear function increase. Meanwhile, a test system is devised to simulate the high-speed collision process between ions and materials, and the derived model is validated through experiments.

Flow of a biomagnetic fluid embedded by magnetic dipole over a continuously moving sheet

AbstractThis paper is concerned with the investigation of steady, two‐dimensional, and laminar boundary layer flow of a biomagnetic fluid over a continuously moving sheet in the presence of a magnetic dipole. The magnetic field resulting from the dipole is contemplated to be strong enough to saturate the biofluid. The magnetization of the fluid is regarded to be a linear function of temperature. The solution procedure involves the reduction of a nonlinear system of coupled PDEs into ODEs that comprise five parameters. The transformed ODEs along with the boundary conditions are then solved numerically by introducing an efficient numerical technique based on the finite difference algorithm. The velocity, as well as temperature profiles within the boundary layer, are illustrated at specified values of free stream velocity (), wall velocity () and ferrohydrodynamic interaction parameter (). The demonstration of the Nusselt number and friction factor are achieved for various governing parameters. Considering a specified Prandtl number () and normalized velocity difference , higher values of the friction factor are obtained for increasing and than that of . Whereas for the Nusselt number, we attain higher values for decreasing and . Moreover, an increase in the velocity ratio results in a decrease in both heat transfer rate as well as friction factor. Furthermore, as increases, the heat transfer rate decreases yet we get higher values for higher and . In the case of friction factor, it increases with increasing and gives higher values for lower and higher . We have also depicted the streamlines for the 2‐D boundary layer flow of the biomagnetic fluid for different . The graphical results manifest that the flow field is greatly impacted by the ferrohydrodynamic field, which could be of interest in medical as well as bioengineering implementations, like, magnetic drug delivery in blood cells, separating RBCs as well as controlling the flow of blood during surgical procedures.

Development of the wave motion induced by near-bottom periodic disturbances in a two-layer shear current

The behavior of wave motion arising in an ideal incompressible homogeneous fluid under switching-on periodic bottom disturbances is studied in the linear approximation for the two-dimensional non-stationary problem. In the undisturbed state, the velocities of two-layer fluid flow are linear functions of the vertical coordinate in each of the layers with different gradients and coincide on the boundary of the layers. The upper boundary of fluid can be either free or bounded by the rigid cover. The dispersion dependences and the group velocities of the appearing wave modes are determined. The vertical displacements of the free surface and the interface between the layers are calculated. A comparison with the solution for a single-layer fluid is carried out.

Data-driven Strategies for Affordable Housing: A Hybrid Genetic Algorithm-Machine Learning Optimization Model in the Melbourne Metropolitan Area

Abstract. The escalating rental crisis in Australia, rooted in demographic dynamics, a scarcity of lands suitable for development and the influence of interest rates and government subsidies, necessitates innovative solutions for housing affordability. One promising approach is to increase the supply of affordable rental housing. Nevertheless, these efforts must be guided by well-informed policies as they are required to cater to the diverse needs of the stakeholders involved. Accordingly, this study aims to prioritize suburbs in the Melbourne Metropolitan area for the construction of apartment/unit buildings, benefiting both builders/investors and renters. Leveraging a hybrid Genetic Algorithm-Machine Learning (GA-ML) framework, multi-objective optimization models are developed to rank 105 suburbs based on key parameters for both builders/investors and renters. The optimization process seeks to maximize economic outlook and rental yields for builders/investors while minimizing rents and commuting distances for renters, in addition to proximity to essential amenities. First, an initial optimization using GA based on six key parameters is performed considering a linear multi-objective function. Subsequently, ML-based objective functions are defined using Random Forest (RF) and extreme Gradient Boosting (XGBoost) models to refine the optimization model for suburb rankings. The evaluation reveals strong correlations between GA and GA-XGB rankings, suggesting the effectiveness of the GA-XGBoost model in prioritizing suburbs. Notably, suburbs consistently prioritized across all models include Brunswick, Coburg, Preston and Reservoir, highlighting their suitability for apartment/unit building construction. By directing attention to specific suburbs aligned with different stakeholders' needs and preferences, this study contributes to a more sustainable and equitable housing landscape.

Optimization Strategies for Rydberg Atom-based AM Receiver Operational Parameters

Abstract The Rydberg atom-based receiver, as a novel type of antenna, demonstrates broad application prospects in the field of microwave communications. However, since Rydberg atomic receivers are nonlinear systems, mismatches between the parameters of the received amplitude modulation (AM) signals and the system's linear workspace and demodulation operating points can cause severe distortion in the demodulated signals. To address this, the article proposes a method for determining the operational parameters based on the mean square error (MSE) and total harmonic distortion (THD) assessments, and presents strategies for optimizing the system’s operational parameters focusing on linear response characteristics (LRC) and linear dynamic range (LDR). Specifically, we employ a method that minimizes the MSE to define the system’s linear workspace, thereby ensuring the system has a good LRC while maximizing the LDR. To ensure the signal always operates within the linear workspace, an appropriate carrier amplitude is set as the demodulation operating point. By calculating the THD at different operating points, the LRC performance within different regions of the linear workspace is evaluated, and corresponding optimization strategies based on the range of signal strengths are proposed. Moreover, to more accurately restore the baseband signal, we establish a mapping relationship between the carrier Rabi frequency and the transmitted power of the probe light, and optimize the slope of the linear demodulation function to reduce the MSE to less than 0.8×10-4. Finally, based on these methods for determining operational parameters, we explore the effects of different laser Rabi frequencies on system performance, and provide optimization recommendations. This research provides robust support for the design of high-performance Rydberg atom-based AM receivers.

Improving the Imbalanced Data Accuracy Using CNN and ReLU

In today’s academic world, learning from datasets is a trendy topic. In the event of imbalanced data, none of the many data mining tools available for this purpose work well, partly because this type of data generates a range of minority classes, which might obstruct the learning process. In addition to its enormous volume, big data has the traits of speed and variety. In this paper, the authors have proposed a CNN model with a rectified linear activation function (ReLU) activation function to get good accuracy on an imbalanced dataset. The dataset used in this paper was electrocardiogram (ECG) heartbeat categorization.

A mathematical model of Cheyne-Stokes or periodic breathing

Cheyne-Stokes Breathing is a periodic cycle of apnea followed by hyperventilation. A theory of this phenomenon is developed based on a minimal set of physiological assumptions. The rate of loss of CO2 from venous blood is proportional to the CO2 concentration in the lungs times the respiration rate; the respiration rate is a linear function of arterial CO2 concentration above a threshold, and zero below that threshold. A time delay between blood in lungs and respiratory response allows the system to go into oscillation. These assumptions lead to a single nonanalytic delay-differential equation containing only three parameters, which we call respiratory recovery coefficients, (α,β,γ). A detailed study of the solutions to this equation is presented here. For β below a first threshold, breathing becomes steady, and any disturbance recovers exponentially to the steady state (∼overdamped oscillator). Above the first threshold, breathing recovers to the steady state by decaying oscillations (∼underdamped oscillator). Above a second threshold, oscillations grow to reach a limit cycle, and when that cycle is sufficiently large, it represents the Cheyne-Stokes cycle of hyperventilation and apnea. Fourier analysis shows that the transition to growing oscillations is a forward or soft Hopf bifurcation. In the Cheyne-Stokes region (sufficiently large β), the equation predicts the shapes of the curves representing the time-dependence of arterial CO2 and the respiration rate. From these shapes, we infer the values of the respiratory recovery coefficients for several groups of patients. With additional approximations, we infer the values of other physiological parameters, including cardiac output, CO2 chemosensitivity, and volume of blood between lungs and detectors.

Design and economic analysis of energy storage optimization allocation for campus microgrid

In the twenty-first century, the "double carbon" plan is advancing steadily. Energy saving and emission reduction is one of the key points of the plan. A power grid independent park, if energy storage equipment can be configured, it can greatly improve the park microgrid power utilization, in order to achieve the purpose of energy saving. Therefore, research on the optimization of the proportion of power grid and microgrid in the park and the optimization of the configuration of energy storage devices can greatly improve the energy utilization rate, so as to achieve the significance of environmental protection. After collecting and sorting the daily load, daily wind power generation and 12-month daily wind power generation data of the three parks A, B and C, and processing the data, a linear function model is established. After using linear programming, operations research and genetic algorithm, the research results are obtained when the three parks are combined and equipped with 50kW/100kWh energy storage devices.

High-temperature transport properties of a two-dimensional weakly doped parabolic semiconductor

A version of the Mexican-hat Hamiltonian is used to study high-temperature transport properties of a two-dimensional weakly doped semiconductor with electron-hole symmetric bands. For a finite doping level and a temperature-dependent band gap, we find a closed analytical form of the temperature-dependent chemical potential. The effective concentrations of charge carriers participating in transport coefficients are analyzed in the space spanned by the total electron concentration and temperature. It is shown that these concentrations are the sum of a residual contribution and two thermally activated contributions, with a complicated dependence on temperature. The analytical expression for the Hall coefficient RHis also found. It is argued that it is a non-monotonic function of the doping level with the maximum at the doping nmax that is a linear function of temperature at high enough temperatures. The analysis of the real part of the interband conductivity shows that it is inversely proportional to incoming photon energy at low temperatures and that it is nearly constant over a wide energy range at high temperatures. This results are expected to be of significant importance in understanding transport and optical properties of weakly doped two-dimensional semiconductors with nearly symmetric parabolic bands.&#xD.

Modeling Water Clusters: Spectral Analyses, Gaussian Distribution, and Linear Function during Time

Our experimental and theoretical studies have consistently revealed the presence of water clusters in various environments, particularly under hydrophobic conditions, where slower hydrogen ion interactions prevail. Crucial methods like Nuclear Magnetic Resonance (NMR) and Fourier Transform Infrared (FTIR) method have played a pivotal role in our understanding of these clusters, unveiling their potential medical applications. The stability and behavior of these clusters can be influenced by factors such as metal ions’ presence, leading to stable clusters’ formation. This potential for medical applications should inspire hope and further research. Moreover, our research has revealed that water clusters exhibit characteristics of dissipative structures, demonstrating the self-organization under physical, chemical, or thermal changes akin to Rayleigh–Benard convection cells. This dynamic and significant behavior supports the notion that water’s role transcends simple chemistry, potentially influencing biological processes at a fundamental level. The interaction of water clusters with their environment and the ability to maintain non-equilibrium states through the energy exchanges further underscores their complexity and significance in both natural and technological contexts. Water filtration is a process for improving water quality. The effect is re-structuring hydrogen bonds and structuring water clusters, most of which are hexagonal. In our research, we applied filtered water using patented EVOdrop Swiss technology.

The analytical curvature distribution model of columns and mathematical solution for pushover analysis

AbstractThe acquisition of a flexural backbone curve for columns primarily relies on finite element analysis and experiments, of which the complexity and high cost are significant challenges. Hence, this study proposes an analytical curvature distribution model (CDM) along the full height of the column, which is the key point of formula derivation and theoretical solution of the column backbone curve. The proposed CDM is a piecewise function model composed of linear and quadratic functions, with the characteristics of continuity and differentiability at the intersection point. The deformation compatibility equations, equilibrium equations, and material constitutive equations based on the variables of CDM are constructed to form an equation system, the solution of which can be theoretically determined by an iterative algorithm. Furthermore, 155 test specimen columns of different materials, for example, reinforced concrete, high‐strength reinforced concrete, and shape memory alloy are used to validate the proposed CDM and mathematical solutions of pushover analysis through three crucial indicators, that is, goodness of fit of backbone curve, ultimate displacement, and peak force, indicating strong practicability, high accuracy, and wider applicability. This theoretical method can be applied to deal with the key issues of interest during pushover analysis, that is, predicting the flexural backbone curves with different materials, determining the curvature distribution throughout the entire process of pushover analysis, and characterizing the evolution process of the plastic region.

Infiltration Characteristics and Hydrodynamic Parameters in Response to Topographic Factors in Bare Soil Surfaces, Laboratory Experiments Based on Cropland Fields of Purple Soil in Southwest China

Topography is an important factor that impacts the hydrological processes on sloping farmlands. Yet, few studies have reported the combined influences of slope gradient and slope position on infiltration characteristics and hydrodynamic parameters on sloping croplands in purple soil regions, an important area for agricultural productivity in Southwest China. Here, laboratory-simulated rainfall experiments were conducted in a steel trough (5 m long, 2 m wide, and 0.45 m deep), and rainfall lasted for 1 h at a rate of 90 mm h−1 to examine the variations in the infiltration rates and hydrodynamic parameters under varying slope gradients (i.e., 3°, 6°, 10°, 15°, 21°, and 27°) and slope positions (i.e., upper, middle, and lower), and explore the relationships between the infiltration rate and the soil detachment rate. The results showed that the infiltration rate decreased gradually with duration rainfall and ultimately approached a steady state in the six slope treatments. Cumulative infiltration ranged from 15.54 to 39.32 mm during rainfall, and gradually reduced with the increase of slope gradient. The Horton’s model outperforms other models for predicting the infiltration rate with an R2 value of 0.86. Factors such as Darcy–Weisbach friction, flow shear force, Manning friction coefficient, unit energy, and runoff depth varied in the following order: upper slope > middle slope > lower slope, whilst the Reynolds number and Froude number gradually increased along the slope transect from the upper to lower slope positions. A significant linear function was fitted between the soil detachment rate and the infiltration rate at the gentle slopes (3°, 6°, 10°), whereas an exponential relationship was observed at the steep slopes (15°, 21°, and 27°). Observation also suggested that 15° was the critical slope gradient of sediment detachment, infiltration characteristics, and hydrodynamic parameters. Our results provide theoretical insight for developing models that predict the impacts of topographic factors on hydrological characteristic and soil erosion in hilly agricultural landscapes of purple soil fields.

Noise-resilient designs and analysis for optical neural networks

Abstract All analog signal processing is fundamentally subject to noise, and this is also the case in next generation implementations of Optical Neural Networks (ONNs). Therefore, we propose the first hardware-based approach to mitigate noise in ONNs. A tree-like and an accordion-like design are constructed from a given Neural Network (NN) that one wishes to implement. Both designs have the capability that the resulting ONNs give outputs close to the desired solution. To establish the latter, we analyze the designs mathematically. Specifically, we investigate a probabilistic framework for the tree-like design that establishes the correctness of the design, i.e., for any feed-forward NN with Lipschitz continuous activation functions, an ONN can be constructed that produces output arbitrarily close to the original. ONNs constructed with the tree-like design thus also inherit the universal approximation property of NNs. For the accordion-like design, we restrict the analysis to NNs with linear activation functions and characterize the ONNs’ output distribution using exact formulas. Finally, we report on numerical experiments with LeNet ONNs that give insight into the number of components required in these designs for certain accuracy gains. The results indicate that adding just a few components and/or adding them only in the first (few) layers in the manner of either design can already be expected to increase the accuracy of ONNs considerably. To illustrate the effect we point to a specific simulation of a LeNet implementation, in which adding one copy of the layers components in each layer reduces the Mean Squared Error (MSE) by 59.1% for the tree-like design and by 51.5% for the accordion-like design. In this scenario, the gap in accuracy of prediction between the noiseless NN and the ONNs reduces even more: 93.3% for the tree-like design and 80% for the accordion-like design.

Experimental adaptive Bayesian estimation for a linear function of distributed phases in photonic quantum networks

The bipartite and multipartite entanglement resources of quantum networks can enhance sensitivity for estimating distributed parameters beyond the classical limits. Recent experimental studies on distributed parameter estimation based on quantum networks have achieved high precision beyond the shot-noise limit (SNL) within certain portions of the parameter space. Towards a realistic distributed parameter estimation scenario, a next key issue is how to achieve the high precision parameter independently with limited measurement data. In this work, we present a photonic experiment employing an efficient Bayesian method to estimate a linear function of four spatially distributed unknown phases. For arbitrary true phase values, our experiment shows the capability of achieving high sensitivities beyond the SNL in a post-selected regime using a restricted amount of measurement rounds. Our work gives a start for the experimental study of distributed adaptive Bayesian quantum estimation. Additionally, this method holds promising utility for more intricate or universal tasks associated with sensing distributed parameters in quantum networks.

Digital image analysis of vertebral body L4 and its ossification center in the human fetus.

Using a Siemens-Biograph 128 mCT camera the morphometric analysis of the L4 vertebral body and its ossification center were done in 55human fetuses aged 17 to 30weeks. No sex differences were found. The mean height, transverse and sagittal diameters of L4 vertebral body followed the logarithmic functions: y = -11.797+ 5.208 × ln(age) ± 0.372, y = -23.462 + 9.428 × ln(age) ± 0.702, y = 2.770 + 13.521 × ln(age) ± 1.722, respectively. The mean cross-sectional area of L4 vertebral body followed the linear function: y = -30.683 + 1.976 × age ± 2.701. The mean volume of L4 vertebral body followed the second-degree polynomial function: y = -93.983+ 0.385 × (age)² ± 23.707. The mean transverse and sagittal diameters of the ossification center of L4 vertebral body followed the natural logarithmic function: y = -27.106 + 10.178 × ln(age) ± 0.769 and y = -13.345 + 5.458 × ln(age) ± 0.424, respectively. The mean cross-sectional area and the volume of the ossification center of L4 vertebral body followed the linear function: y = -30.683 + 1.976 × age ± 2.701 and y = -43.214 + 2.760 × age ± 4.085, respectively.

Solutions to insufficient incentives for developing green tourism by travel agencies: government intervention

PurposeThis research aims to develop an improved model with government intervention and find the government policy for developing green tourism to induce the travel agencies have incentives to produce green tourism products.Design/methodology/approachThis research employs Stackelberg game theory to study two travel agencies in the horizontal direction of the tourism supply chain. Two deterministic, price-sensitive linear demand functions are utilized for these two different tourism products to derive possible analytical solutions.FindingsNo travel agency is willing to produce green tourism products without government intervention. The solution proposed in this paper is that a government should subsidize green travel agencies for their production of green tourism products, and create a tax for non-green traditional travel agencies for the production of non-green traditional tourism products. The amount of government subsidies for green tourism products plus the tax on non-green traditional tourism products equals the difference in unit cost of the two products. The travel agency that produces green tourism products has incentive to produce if there is government intervention.Practical implicationsThis paper provides the stakeholders with three practical implications. The first one is that the amount of subsidy for green travel agencies can be paid by taxing non-green ones. This is the optimal solution. The second one for both the tourism sector and government is that technological innovation in cooperation between government and tourism industry such as low-carbon technology is critical to reduce the cost difference between green travel agency products and non-green ones. The third one is that green travel agencies that produce green tourism products can also fulfill their corporate social responsibilities and enhance their social image.Originality/valueThis paper is unique in that it develops a model to resolve the problem of insufficient incentives. In terms of government intervention, this article also considers tax policy in addition to subsidy policy which is different from previous literature.

Dielectric metasurface Fresnel zone plates for polarization conversion

Abstract Conventional Fresnel zone plates (FZPs) can only achieve a single focusing function and require the combination with other optical elements to achieve multiple optical functions. This contradicts the development trends for miniaturized, integrated and multifunctional optical devices. However, the emergence of metasurfaces offers new solutions for this problem. In this paper, we design two different types of multifunctional metasurface Fresnel zone plates (MFZPs). One is based on amplitude modulation, and the other is based on phase modulation, both of which can achieve linear polarization conversion and focusing functions. The realization of these functions is based on the ability of silicon diatomic nanopillars to decouple and control the amplitude, phase, and polarization of electromagnetic waves. The designed ultrathin dielectric metasurface effectively combines the functions of conventional half-wave plates and FZPs, thereby reducing the volume of the optical system. The designed MFZPs have enormous potential for application in integrated and compact optical systems.

Age-dependent changes in the hyoid bone morphology in children.

This radiologic work aimed to display the alteration in the hyoid bone (HB) morphology in the pediatric population with advancing age. This pediatric examination consisted of computed tomography images of 129 subjects (49 males / 80 females) aged 1-17 years. The anterior-posterior length of HB, the lengths of right and left greater horns, the width and height of HB's body, and the distance between the midpoints of the posterior ends of the greater horns increased with advancing age (p < 0.001), but the angle of the right and left greater horns (p = 0.022) decreased. Four configurations regarding HB shape were observed: Type A (U-shaped HB) in 8.5% (11 HBs) out of 129 children, Type B (B-shaped HB) in 33.3% (43 HBs), Type C (D-shaped HB) in 45% (58 HBs), and Type D (V-shaped HB) in 13.2% (17 HBs). HB shape types correlated with the pediatric age (p < 0.001), but not gender (p = 0.153). Most of the parameters increased until the postpubescent period, but the angle of the right and left greater horns decreased after the late childhood. Our linear functions representing the growth pattern of HB in children may be useful to estimate HB size.