Multistep Methods Research Articles

A New Methodology for the Development of Efficient Multistep Methods for First-Order Initial Value Problems with Oscillating Solutions: III the Role of the Derivative of the Phase Lag and the Derivative of the Amplification Factor

A New Methodology for the Development of Efficient Multistep Methods for First-Order Initial Value Problems with Oscillating Solutions: III the Role of the Derivative of the Phase Lag and the Derivative of the Amplification Factor

The influence of multi-step modification method on the adsorption effect of alkali metal adsorbent in high temperature corrosive environment

In order to mitigate the serious high-temperature corrosion problem caused by gaseous alkali metal salts on the heating surface of boilers, the adsorption effect of kaolinite for alkali metal vapor stood out among many silicon-aluminum-based adsorbents. To improve the adsorption capacity of kaolinite for alkali metal vapor, a novel multi-step modification method was proposed in this reported work. The multi-step modification method consisted of the following four steps, which were pre-intercalation, replacement intercalation, multiple intercalation, and exfoliation, and it was found that the multi-step modification method resulted in the increase of the particle size, the expansion of the interlayer spacing, and the expansion of the porosity structure of kaolinite. The physicochemical analyses showed that the multi-step modification method made it easier to dehydrate kaolinite to produce metakaolinite. In addition, it was found that the multi-step modification method led to the generation of a new crystalline phase of kaolinite, which was formed by the dehydration and condensation of methanol and AlOH groups. It also led to the pre-removal of some of the hydroxyl groups in kaolinite. The insoluble sodium loading capacity of the multi-step modified kaolinite was enhanced by 64.47% and the insoluble potassium loading capacity was enhanced by 29.68% under the adsorption condition of 850 °C for 45 min. Therefore, the multi-step modification method enhanced the alkali metal vapor adsorption capacity of raw kaolinite under high-temperature environment, which laid a certain foundation for subsequent research in this field.

Mathematical modeling of neuron model through fractal-fractional differentiation based on maxwell electromagnetic induction: application to neurodynamics

The electrical activities of the reliable neuron models have different responses within intrinsic biophysical effects and can functionalize for asymmetric coexisting electrical activities under anti-monotonicity phenomenon. This manuscript presents mathematical analysis of neuron model based on Maxwell electromagnetic induction through newly proposed fractal-fractional differential and integral operators. The neuron model based on Maxwell electromagnetic induction changes with time along a fractal dimension that describes the cumulative chaotic phenomenon. The cumulative chaotic phenomenon of neuron model is mathematically modeled via exponential and Mittag–Leffler kernels with variable and fixed fractal and fractional orders. In order to exhibit fractal properties and memory effects, the neuron model is discretized by means of Adams–Bashforth-Moulton method that allows explicitly to compute the approximate solution of neuron model. The comparison of neuron model based on memory effect and fractal dimension have distinguished the evolution of neuron model at (i) variability of fractal order with fixed fractional order, (ii) variability of fractional order with fixed fractal order, and (iii) variability of fractal order as well fractional order.

APPN: An Attention-based Pseudo-label Propagation Network for few-shot learning with noisy labels

Few-shot learning has garnered significant attention in deep learning as an effective approach for addressing the issue of data scarcity. Conventionally, training datasets in few-shot learning are clean. However, due to the occurrence of sensor malfunctions, data transmission anomalies, or inaccuracies in manual annotation, the accuracy of sample annotations cannot be guaranteed. Therefore, dealing with few-shot learning with noisy label becomes an urgent problem. To solve the above problem, we propose an Attention-based Pseudo-label Propagation Network (APPN). We make some technical contributions: (1) We propose an attention-based feature extraction method that can effectively capture the distinctions between clean and noisy samples. (2) We propose an improved graph-based pseudo-label propagation method that utilizes pseudo-labels with latent class information as initial labels, thereby enhancing the accuracy of label propagation. (3) We describe a comprehensive multi-step noise detection method which can accurately detect noisy samples from clean samples and effectively distinguish between out-of-domain (OOD) noise and in-domain (ID) noise. (4) Finally, the solid experiments verify the better performance on FC100, CIFAR-FS, miniImageNet, and tieredImageNet datasets. The results show that our method has high robustness and superiority in the few-shot learning with noisy labels. Code and models at: https://github.com/Typistchen/APPN.

One-Step Hydrothermal Deposition of AgSbS2-xSex Thin Films for Solar Cell Applications.

AgSbS2-xSex is a promising light-harvesting material for thin film solar cells, characterized by nontoxicity, high chemical stability, and excellent optoelectronic properties. However, the complex chemical composition of AgSbS2-xSex poses significant challenges to thin film preparation, giving rise to an intensive dependence on multi-step preparation methods. Herein, a hydrothermal method is developed for depositing AgSbS2-xSex films and achieves one-step preparation of this kind of thin film materials for the first time. This method can provide sufficient energy for atomic nucleation and adsorption on the substrate surface to promote nuclei aggregation and grow into films. Meanwhile, it achieves control of the chemical kinetics of the deposition solution by introducing EDTA-2Na as an additive and suppressing the enrichment of Ag2Se impurities at the substrate interface. As a result, a high-purity AgSbS2-xSex film with compact and flat morphology is prepared and assembled into solar cells. The device delivers a power conversion efficiency of 3.04% under standard illumination, which is currently the highest efficiency for AgSbS2-xSex solar cells fabricated by the one-step method. This study provides a facile and promising method for the controllable preparation of high-quality AgSbS2-xSex thin films and promoting their application in solar cells.

Implementing the predictor-corrector approach to examine the thermo-solutal convection for buongiorno eyring-powell nanofluid model with squeezed microcantilivier surface

The Buongiorno nanofluid model serves as a foundational model for theoretical and experimental research in the field of nanofluids, and this model can be applied to various engineering problems, including heat exchangers, biomedical applications, solar collectors, nuclear reactors, and different cooling systems in the automotive and electronics industries. The use of nanofluids in the Eyring-Powell fluid over a squeezed sensing surfaces is a vital area of research for the design and improvement of microfluidic devices and sensors, which find widespread usage in industrial and medical applications. The main purpose of this work is to note the augmentation in thermal conductivity by using the Buongiorno nanofluid model along with the natural convective flow of non-Newtonian Eyring-Powell fluid that is moving on the squeezed sensory surface along with slip velocity. The viscosity of a fluid is assumed to be dependent on temperature. The Cattaneo-Christov heat and mass flux and chemical reaction are assumed to determine the combined effect of heat and mass transport. The governing model of equations is in the form of dimensional partial differential equations, and we have to convert these equations into ordinary differential equations; therefore, a set of similarity transformations is adopted for making the equations into dimensionless form. The numerical results were obtained by adopting the predictor and corrector multistep method, namely the ‘Adams-Bashforth’ technique, in Matlab software. The use of natural convective flow enhances the velocity region. The velocity slip parameter increases the velocity of the fluid, whereas the viscosity parameter drops the velocity profile. The thermophoresis and Brownian motion parameters are the sources of the increment in the temperature region. The thermal relaxation and solutal relaxation parameters are the sources of decline in the temperature region. The squeezing parameter is the source of reduction in the skin friction, whereas the result indicates that the fluid parameter, Grashof number, and viscosity coefficients increase the skin friction.

Preparation of Highly Efficient and Stable All-Inorganic CsPbBr3 Perovskite Solar Cells Using Pre-Crystallization Multi-Step Spin-Coating Method

All-inorganic CsPbBr3 perovskite solar cells have garnered extensive attention in the photovoltaic domain due to their remarkable environmental stability. Nevertheless, CsPbBr3 prepared using the conventional sequential deposition method suffers from issues such as inferior crystallinity, low phase purity, and poor film morphology. Herein, we propose a pre-crystallization methodology by introducing a minute quantity of CsBr into the PbBr2 precursor solution to generate a small amount of CsPb2Br5 crystals within the PbBr2 film, leading to a porous PbBr2 film with enhanced crystallinity. Under the influence of more pores and CsPb2Br5 crystals as nucleation sites for inducing growth, a CsPbBr3 film with a larger crystal size, lower grain boundary density, stronger crystallinity, and higher phase purity is formed. Compared with untreated devices, photovoltaic devices prepared using the pre-crystallization method achieved a champion photovoltaic conversion efficiency (PCE) of 8.62%. Furthermore, pre-crystallized devices demonstrate higher stability than untreated ones and can still retain 94% of the original PCE after being exposed to air for 1000 h without encapsulating.

Supercooled large droplet size distribution effects on airfoil icing: A numerical investigation based on a new coupled Eulerian method

Supercooled large droplets (SLDs) under natural icing conditions have the characteristics of easy deformation in motion and easy splashing on impact, and a bimodal droplet size distribution that has received less attention. The modified form of the Rosin-Rammler function was improved to achieve a more accurate nonlinear fitting of the SLD distribution curve. The droplet size distribution was divided into non-equipartition continuous multiple components. The drag source term of each component was coupled with the overall droplet size distribution, and the Eulerian equations of each component of SLDs were solved simultaneously. A new coupled Eulerian method for non-equipartition continuous multi-size droplets was proposed to simulate the impact characteristics of SLDs, and the SLD collection coefficients were validated. Effects of the ratio between the number of large and small droplet components and the number of all components on the simulation results were investigated to select a better combination based on stable convergence calculation steps and the calculation time. This new method was added to the multi-step icing numerical method, and the accuracy and robustness of the method in icing shape prediction were verified based on the freezing drizzle, median volume diameter < 40 μm (FZDZ, MVD < 40 μm) icing condition. Airfoil icing characteristics based on the bimodal and monomodal distribution were compared, and the icing shapes at the leading edge were similar. Still, the upper and lower limits of the icing shapes with the bimodal distribution were nearer to the trailing edge and the ice layer was thicker there.

Monitoring of water volume in a porous reservoir using seismic data: A 3D simulation study

A potential framework to estimate the volume of water stored in a porous storage reservoir from seismic data is neural networks. In this study, the man-made groundwater reservoir is modeled as a coupled poroviscoelastic–viscoelastic medium, and the underlying wave propagation problem is solved using a three-dimensional discontinuous Galerkin method coupled with an Adams–Bashforth time stepping scheme. The wave problem solver is used to generate databases for the neural network-based machine learning model to estimate the water volume. In the numerical examples, we investigate a deconvolution-based approach to normalize the effect from the source wavelet in addition to the network's tolerance for noise levels. We also apply the SHapley Additive exPlanations method to obtain greater insight into which part of the input data contributes the most to the water volume estimation. The numerical results demonstrate the capacity of the fully connected neural network to estimate the amount of water stored in the porous storage reservoir.

Enhancing Water Pollution Management Through a Comprehensive Fractional Modeling Framework and Optimal Control Techniques

Water pollution poses a significant threat to public health, particularly in developing nations. This study aims to enhance our understanding of water pollution transmission dynamics by introducing a novel mathematical model within a general fractional framework. The model offers a comprehensive analysis, including assessing solution feasibility and the stability of equilibrium points. To effectively implement this model, we develop an efficient numerical scheme based on the trapezoidal method. Furthermore, we conduct a thorough error discussion and convergence analysis. Notably, we devise and evaluate a new strategy to effectively tackle the associated fractional optimal control problem concerning water pollutant transmission. Applying this approach to a real case demonstrates its substantial impact, notably in reducing non-soluble contaminants within the water transmission system.

Direct Zeptomole Detection of RNA Biomarkers by Ultrabright Fluorescent Nanoparticles on Magnetic Beads.

Nucleic acids are important biomarkers in cancer and viral diseases. However, their ultralow concentration in biological/clinical samples makes direct target detection challenging, because it leads to slow hybridization kinetics with the probe and its insufficient signal-to-noise ratio. Therefore, RNA target detection is done by molecular (target) amplification, notably by RT-PCR, which is a tedious multistep method that includes nucleic acid extraction and reverse transcription. Here, a direct method based on ultrabright dye-loaded polymeric nanoparticles in a sandwich-like hybridization assay with magnetic beads is reported. The ultrabright DNA-functionalized nanoparticle, equivalent to ≈10 000 strongly emissive rhodamine dyes, is hybridized with the magnetic bead to the RNA target, providing the signal amplification for the detection. This concept (magneto-fluorescent sandwich) enables high-throughput detection of DNA and RNA sequences of varied lengths from 48 to 1362nt with the limit of detection down to 0.3 fm using a plate reader (15 zeptomoles), among the best reported for optical sandwich assays. Moreover, it allows semi-quantitative detection of SARS-CoV-2 viral RNA directly in clinical samples without a dedicated RNA extraction step. The developed technology, combining ultrabright nanoparticles with magnetic beads, addresses fundamental challenges in RNA detection; it is expected to accelerate molecular diagnostics of diseases.

Multistep Iterative Methods for Solving Equations in Banach Space

The novelty of this article lies in the fact that we extend the use of a multistep method for developing a sequence whose limit solves a Banach space-valued equation. We suggest the error estimates, local convergence, and semi-local convergence, a radius of convergence, the uniqueness of the required solution that can be computed under ω-continuity, and conditions on the first derivative, which is on the method. But, earlier studies used high-order derivatives, even though those derivatives do not appear in the body structure of the proposed method. In addition to this, they did not propose computable estimates and semi-local convergence. We checked the applicability of our study to three real-life problems for semi-local convergence and two problems chosen for local convergence. Based on the obtained results, we conclude that our approach improves its applicability and makes it suitable for challenges in applied science.

Achieving Optimal Order in a Novel Family of Numerical Methods: Insights from Convergence and Dynamical Analysis Results

In this manuscript, we introduce a novel parametric family of multistep iterative methods designed to solve nonlinear equations. This family is derived from a damped Newton’s scheme but includes an additional Newton step with a weight function and a “frozen” derivative, that is, the same derivative than in the previous step. Initially, we develop a quad-parametric class with a first-order convergence rate. Subsequently, by restricting one of its parameters, we accelerate the convergence to achieve a third-order uni-parametric family. We thoroughly investigate the convergence properties of this final class of iterative methods, assess its stability through dynamical tools, and evaluate its performance on a set of test problems. We conclude that there exists one optimal fourth-order member of this class, in the sense of Kung–Traub’s conjecture. Our analysis includes stability surfaces and dynamical planes, revealing the intricate nature of this family. Notably, our exploration of stability surfaces enables the identification of specific family members suitable for scalar functions with a challenging convergence behavior, as they may exhibit periodical orbits and fixed points with attracting behavior in their corresponding dynamical planes. Furthermore, our dynamical study finds members of the family of iterative methods with exceptional stability. This property allows us to converge to the solution of practical problem-solving applications even from initial estimations very far from the solution. We confirm our findings with various numerical tests, demonstrating the efficiency and reliability of the presented family of iterative methods.

A Fuzzy Optimal Base Stock System for Tolerant Clients

Base stock is an amount of stock that a company requires to maintain in order to handle an unexpected huge demand. To lerant clients are the clients who are tolerant to the company’s delayed supply, who come back to the same company even if their demands are not met within their expected time. This implies that the clients are solely relied on that company. Marketing manager requires to maintain on hand to satisfy such tolerant clients’ demands with some delay, no longer than expected by that tolerant client.This paper diagnosis the performance measures of optimal base stock system for tolerant clients in fuzzy environment. The fuzzy numbers can be modified to crisp number with the help of fuzzy ranking methods. Here the used fuzzy ranking method is prominent for de-fuzzification. The famous Triangular fuzzy number and Trapezoidal fuzzy number methods are played a major role for de-fuzzification. At last, the optimization of base stock is verified with numerical examples in fuzzy environment.

Raspberry ketone loaded self nanoemulsifying system of cardamom oil: Assessment of phase behavior, dissolution rate and anti-hyperlipidemic activity

Raspberry ketone (RK), a polyphenolic antioxidant, possesses free radical scavenging against oxidative species and has potential of anti-inflammatory, anti-proliferative and anti-aging activities. Major pharmaceutical restriction associated with RK is its poor dissolution characteristic owing to its hydrophobic nature. Present investigation is an attempt to improve dissolution behavior of RK using cardamom oil (CO) based self nanoemulsifying system (SNE) design and preclinical assessed for anti-hyperlipidemic activity. Demarcation of phase boundaries to exactly locate nanoemulsion areas were explored using ternary plots drawn between CO as oil phase, Tween 80/PEG 600 as Smix at 1:1; 1:2; 2:1 and 3:1 ratios. Previously ternary components were selected on the basis of solubility of RK and aqueous dispersibility of CO. Nanoemulsion areas developed under ternary phase region were quantified using trapezoidal method and found in the order 1:1 > 1:2 > 3:1 > 2:1 of Smix. Aqueous dilutibility of SNEs followed the pattern of dilutions lines drawn across the ternary phase and its interference. Optimized SNE produced 97.1 % transmittance with average droplet size 101 nm, zeta potential −2.27 mV and 0.186 mS/cm conductivity. In-vitro RK release was examined in HCl buffer at pH 1.2 and phosphate buffer at pH 6.8 showed a significant difference in the RK dissolved (p < 0.01) compared to RK suspension (control F6). Optimized formulation (F3) at two doses level (RK loading of 80 and 160 mg/kg) vs. RK suspension (160 mg/kg) was pre-clinically administered for four weeks to assess anti-hyperlipidemic activity. Lipid profile markers (levels of VLDL, HDL, LDL, total triglyceride and total cholesterol) were significantly reduced from nanoemulsion formulation as compared to its suspension. SNE formulations were stable with no appreciable loss in quality and performance for six month storage at 30 ± 2 °C; 65 ± 5 % RH conditions. CO based SNE design significantly extended the ternary area for nanoemulsion development as well as RK solubility; which in turn improved dissolution rate of RK and showed anti-hyperlipidemic activity.

Development of Neurospecific Assessment Scale for Nomophobics – An Observational Study

Abstract Background: Nomophobia is a condition where people feel anxious or tense when they need to disconnect from their phone or other Internet-connected devices. Because of this elevated level of dependence on modern gadgets to offload the cognitive demands of life, anxiety develops when they are expected to be detached from it. The role of neurospecific domains such as cognitive flexibility, memory, attention, information processing, inhibitory control, and reward perception has previously been studied in nomophobics. However, there is no tool developed yet that quantifies the affection of these neurospecific domains in nomophobics. Objective: The objective of this study was to develop a scale for the assessment of “Neurospecific Domains” (in terms of memory, attention, cognitive flexibility, inhibitory control, information processing, and reward perception) among nomophobics. Methods: The neurospecific assessment scale for nomophobics (NSASN) was developed using a multistep method which included conceptualization and item generation followed by one round of expert validation of the item and of the scale. The content validity index was used to validate the various domains in the scale. Results: The computed content validity final score for Round 1 of the scale was found to be 0.79. Conclusion: The NSASN was developed to assess neurospecific domains among nomophobics and achieved a statistically satisfactory content validity.

Numerical approximation of a generalized time fractional partial integro-differential equation of Volterra type based on a meshless method

The moving least squares (MLS) approximation is used in this study to solve time-fractional partial integro-differential equations (TFPIDE). In our approach, we approximate the time Caputo fractional derivative term and the integral term by using a finite difference scheme and trapezoidal method, respectively, which yields an order of accuracy of O(τ+τ2−α), where 0<α<1. We thoroughly investigate the applicability and validity of the proposed method and provide an error estimate for its performance. Additionally, we solve various numerical problems to demonstrate the accuracy and computational efficiency of our approach, confirming the theoretical findings.

Analyzing crop production: Unraveling the impact of pests and pesticides through a fractional model

The continuous growth of the human population raises concerns about food, fiber, and agricultural insecurity. Meeting the escalating demand for agricultural products due to this population surge makes protecting crops from pests becomes imperative. While farmers use chemical pesticides as crop protectors, the extensive use of these chemicals adversely affects both human health and the environment. In this research work, we formulate a nonlinear mathematical model using the Caputo fractional (CF) operator to investigate the effects of pesticides on crop yield dynamics. We assume that pesticides are sprayed proportional to the density of pest density and pests not entirely reliant on crops. The feasibility of every possible nonnegative equilibrium and its stability characteristics are explored utilizing the stability theory of fractional differential equations. Our model analysis reveals that in a continuous spray approach, the roles of pesticide abatement rate and pesticide uptake rate can be interchanged. Furthermore, we have identified the optimal time profile for pesticide spraying rate. This profile proves effective in minimizing both the pest population and the associated costs. To provide a practical illustration of our analytical findings and to showcase the impact of key parameters on the system’s dynamics, we conducted numerical simulations. These simulations are conducted employing the generalized Adams–Bashforth–Moulton method, which allowed us to vividly demonstrate the real-world implications of our research.

Analyzing crop production: Unraveling the impact of pests and pesticides through a fractional model

The continuous growth of the human population raises concerns about food, fiber, and agricultural insecurity. Meeting the escalating demand for agricultural products due to this population surge makes protecting crops from pests becomes imperative. While farmers use chemical pesticides as crop protectors, the extensive use of these chemicals adversely affects both human health and the environment. In this research work, we formulate a nonlinear mathematical model using the Caputo fractional (CF) operator to investigate the effects of pesticides on crop yield dynamics. We assume that pesticides are sprayed proportional to the density of pest density and pests not entirely reliant on crops. The feasibility of every possible nonnegative equilibrium and its stability characteristics are explored utilizing the stability theory of fractional differential equations. Our model analysis reveals that in a continuous spray approach, the roles of pesticide abatement rate and pesticide uptake rate can be interchanged. Furthermore, we have identified the optimal time profile for pesticide spraying rate. This profile proves effective in minimizing both the pest population and the associated costs. To provide a practical illustration of our analytical findings and to showcase the impact of key parameters on the system’s dynamics, we conducted numerical simulations. These simulations are conducted employing the generalized Adams–Bashforth–Moulton method, which allowed us to vividly demonstrate the real-world implications of our research.

Numerical Simulation Model of the Infectious Diseases by Comparing Backward Euler Method and Adams-Bash forth 2-Step Method

In this work, the Backward Euler technique and the Adams-Bashforth 2-step method—two numerical approaches for solving the SIR model of epidemiology are compared for performance. An essential resource for comprehending the transmission of infectious illnesses like COVID-19 in the SIR model. While the explicit Adams-Bash forth 2-step approach is well known for its computing efficiency, the implicit Backward Euler method is noted for its stability. The study evaluates the accuracy, strength, and computing cost of the two approaches to determine which approach is best for simulating the spread of infectious illnesses. The SIR Model was easily solved using the Adams Bashforth 2-step analysis and the Backward Euler method. The approaches' solutions are close to the exact requirements. There are important distinctions between the two-step Adams Bashforth and backward Euler procedures. The running time of the Adams Bashforth 2-step backward Euler method is shorter than that of the backward Euler method.