Equation Approach Research Articles

Highly dispersive eighth-order embedded solitons with cubic–quartic χ(2) and χ(3) nonlinear susceptibilities under the influence of multiplicative white noise using Itô calculus

This research explores the intriguing realm of eighth-order embedded solitons in highly dispersive media with cubic–quartic nonlinear susceptibilities [Formula: see text] and [Formula: see text], all within the dynamic context of multiplicative white noise and the framework of Itô calculus. Two different approaches are used in this study. The new auxiliary equation approach produces the bright soliton and singular soliton solutions, while the addendum Kudryashov’s approach produces the bright soliton, singular soliton and combo bright–singular soliton solutions. The system under investigation and the results documented within this work stand as pioneering and original contributions to the field of nonlinear optics. Furthermore, a collection of 2D, 3D and contour plots is produced to visually represent the spatial distribution and progression of different solutions. This not only contributes to the advancement of nonlinear equations in theory but also offers valuable insights for practical applications.

Spin-polarization and Coulomb interaction dependent thermal rectification in a quantum dot system

Abstract Based on the master equation approach, we investigate the thermal transport through a diode composed of a quantum dot under Coulomb interaction and tunnel-coupled to two ferromagnetic leads with antiparallel spin polarizations. We analyze the effects of spin polarizations, Coulomb interaction, mean temperature and Zeeman splitting on the thermal rectification. Firstly, we find that the thermal rectification effect is enhanced with the increase of spin polarization, because the mirror-symmetry of the system is broken by the anti-parallel spin polarization. Especially, when both leads are fully spin polarized, the asymmetry of the heat transferred by Coulomb interaction under the opposite temperature bias leads to the appearance of perfect thermal rectification and negative differential thermal conductance. Secondly, we find whether the system is in a Coulomb blockade state greatly affects the thermal rectification coefficient. As the average temperature increases or the intradot Coulomb interaction decreases, the system gradually escapes from the Coulomb blockade state, resulting in a reversal of the thermal rectification direction and ultimately leading to an increase in the rectification coefficient. Thirdly, we also find that the Zeeman splitting can be utilized to modulate the behavior of thermal rectification. Thermal rectification occurs only when Zeeman splitting and spin polarization coexist, and under different spin polarizations, the rectification coefficient exhibits different trends with the change of Zeeman splitting. These observations indicate that this structure holds potential application at a thermal rectifier as well as a thermal detector of magnetic fields.

Does chubby can get lower grades than skinny Sophie? Using an intersectional approach to uncover grading bias in German secondary schools.

We aim to uncover grading bias by gender, socio-economic status, ethnic/migration background as well as body weight in the German secondary school system. Following an intersectional approach, we test whether-controlling for ability-students receive different grades depending on (the specific combination of) ascriptive characteristics. Using data from the fourth starting cohort (SC4, 13.0.0, first survey in year 9 in 2010) of the National Educational Panel Study (NEPS) consisting of more than 14,000 ninth graders, we compute the predicted differences in grades for the different groups of students depending on whether they are a boy or a girl, whether they are obese/overweight or not, their socio-economic status (SES) and ethnic background. We rely on a grade equation approach, assuming that discrepancies between observed grades and achievement as measured in standardised tests are evidence of biased grading. We control for two different competence tests-the Domain General Cognitive Functions (DGCF) and a standardised domain-specific competence test-as objective measures of ability as well as secondary school track. Even after controlling for different personality and behavioural traits-the "big five", the Strengths and Difficulties Questionnaire (SDQ), the Sick, Control, One, Fat and Food (SCOFF), health satisfaction and class retention-substantial differentials in grading across almost all factors and subjects remain. To account for the fact that many students may face bias on multiple grounds, we then compare the differences in predicted grades for groups with overlapping (dis)advantaging characteristics (e.g. low SES overweight Turkish boy vs a high SES non-overweight majority girl), while controlling for the objective ability measures. Significant differentials in grades are found in almost all cases, with the largest effect sizes for the subject German. We also compute models including all 2-way or 4-way interactions between the four axes of inequality and find the main effects largely unchanged. On the whole our findings are indicative of widespread additive intersectional effects of gender, social and ethnic origin as well as body weight on grading bias.

Optical soliton solution of the perturbed Biswas-Milovic equation having cubic-quintic-septic law nonlinearity in the presence of spatio-temporal and chromatic dispersion

Abstract In this manuscript, we investigate the analytical and soliton solutions of the cubic-quintic-
septic law for the perturbed Biswas-Milovic equation, considering spatio-temporal and chro-
matic dispersions. The perturbed Biswas-Milovic equation with the spatio-temporal and
chromatic dispersion terms provides a comprehensive study for describing nonlinear opti-
cal wave propagation in optical fiber. We use the wave transformation to reduce the main
equation to a nonlinear ordinary differential equation. Through the transformation of the
original equation into a more simplified form, it aims to attain a more profound comprehen-
sion of the fundamental dynamics of the system. We retrieve the analytical solutions of the
presented model by implementing the new Kudryashov technique and a subversion of the
new extended auxiliary equation approach. Besides, bright, singular, and V-shape soliton
structures are represented. Moreover, we analyze the soliton behavior influenced by various
parameters. The analysis of the parameter influences reveals the complicated relationship
governing the dynamics of the perturbed Biswas-Milovic model.

Multilevel Interventions and Dental Attendance in Pediatric Primary Care: A Cluster Randomized Clinical Trial.

Untreated tooth decay is disproportionately present among low-income young children. While American Academy of Pediatrics (AAP) guidelines require pediatric clinicians to implement oral health care, the effectiveness of these oral health interventions has been inconclusive. To test the effectiveness of multilevel interventions in increasing dental attendance and reducing untreated decay among young children attending well-child visits (WCVs). The Pediatric Providers Against Cavities in Children's Teeth study is a cluster randomized clinical trial that was conducted at 18 pediatric primary care practices in northeast Ohio. The trial data were collected between November 2017 and July 2022, with data analyses conducted from August 2022 to March 2023. Eligible participants included Medicaid-enrolled preschoolers aged 3 to 6 years attending WCVs at participating practices who were enrolled at baseline (WCV 1) and followed-up for 2 consecutive examinations (WCV 2 and WCV 3). Clinicians in the intervention group received both the practice-level (electronic medical record changes to document oral health) and clinician-level (common-sense model of self-regulation theory-based oral health education and skills training) interventions. Control group clinicians received AAP-based standard oral health education alone. Dental attendance was determined through clinical dental examinations conducted by hygienists utilizing International Caries Detection and Assessment System criteria and also from Medicaid claims data. Untreated decay was determined through clinical examinations. A generalized estimating equations (GEE) approach was used for both clinical examinations and Medicaid claims data. Eighteen practices were randomized to either intervention or control. Participants included 63 clinicians (mean [SD] age, 47.0 [11.3] years; 48 female [76.2%] and 15 male [23.8%]; 28 in the intervention group [44.4%]; 35 in the control group [55.6%]) and 1023 parent-child dyads (mean [SD] child age, 56.1 [14.0] months; 555 male children [54.4%] and 466 female children [45.6%]; 517 in the intervention group [50.5%]; 506 in the control group [49.5%]). Dental attendance from clinical examinations was significantly higher in the intervention group (170 children [52.0%]) vs control group (150 children [43.1%]) with a difference of 8.9% (95% CI, 1.4% to 16.4%; P = .02). The GEE model using clinical examinations showed a significant increase in dental attendance in the intervention group vs control group (adjusted odds ratio, 1.34; 95% CI, 1.07 to 1.69). From Medicaid claims, the control group had significantly higher dental attendance than the intervention group at 2 years (332 children [79.6%] vs 330 children [73.7%]; P = .04) but not at 3 years. A clinically but not statistically significant reduction in mean number of untreated decay was found in the intervention group compared with controls (B = -0.27; 95% CI, -0.56 to 0.02). In this cluster randomized clinical trial, children in the intervention group had better dental outcomes as was evidenced by increased dental attendance and lower untreated decay. These findings suggest that intervention group clinicians comprehensively integrated oral health services into WCVs. ClinicalTrials.gov Identifier: NCT03385629.

Pell Collocation Approach for the Nonlinear Pantograph Differential Equations

Pantograph equations, which we encounter in the branches of pure and applied mathematics such as electrodynamics, control systems and quantum mechanics, are essentially a particular form of the functional differential equations characterized with proportional delays. This study focuses on exploring the approximate solution to the Pantograph differential equation. Since there is no analytic solutions for this equation class, only the approximate solutions can be obtain. For this purpose, Pell Collocation Method which is one of the numerical solution methods is chosen. As the result of applying the method to the equation, an algebraic equation system has been gained and then the approximate solution has been found by using MATHEMATICA via the given initial conditions. The method is applied to the some test examples and then the results are presented by both graphically and by table. The error estimations show that the method works accurately and efficiently.

SOCIOECONOMIC MODEL OF SHELLFISH RESOURCES IN SEMBILANG NATIONAL PARK BANYUASIN REGENCY SOUTH SUMATRA

The Sembilang National Park area has blood cockle (Anadara granosa) resources. Catching blood cockles is done traditionally, namely using hands at low tide. To maintain shellfish resources, it is necessary to analyze the factors that influence socioeconomic catches. The aim of this research is to calculate and analyze the factors that influence and determine the best socio-economic model for shellfish resources in Sembilang National Park. This research was carried out in February 2022 in the waters of Sembilang National Park. Determining the number of respondents and collecting data in this study used the incidental sampling method and data collection was carried out by interviews using questionnaires. Model assumption testing includes normality test, linearity test, multicollinearity test, heteroscedasticity test and autocorrelation test. Best fit model uses a multiple linear regression equation approach with the backward analysis regression method, namely Y = -1456.315 + 0.116X1 + 1.514 X2 + 2.547 X3 - 12.558 X 7 + ε. Factors that influence the number of catches of shellfish resources in Sembilang National Park, Banyuasin Regency are the selling price of shellfish, operating costs, income and number of dependents. Keywords: Shellfish resources, best fit model, Sembilang National Park, Socioeconomics.

Unraveling the mechanism of assimilatory nitrate reduction and methane oxidation by Methylobacter sp. YHQ through dual N-O isotope analysis and kinetic modeling

Assimilatory nitrate reduction and methane (CH4) oxidation by bacteria play important roles in carbon (C) and nitrogen (N) biogeochemical cycles. Here, an investigation of enzymatic assimilatory nitrate reduction and CH4 oxidation by Methylobacter sp. YHQ from the wetlands is presented, specifically concentrating on N and oxygen (O) isotope fractionation with various initial nitrate and oxygen concentrations. The N enrichment factors (15εassimilation) increased from 4.2 ± 0.7‰ to 6.9 ±1.3‰ and the O isotope enrichment factors (18εassimilation) increased from 2.7 ± 0.9‰ to 4.7 ± 0.8‰ during nitrate assimilation when initial nitrate concentrations increased from 0.9 mM to 2 mM. Similar 18ε and 15ε values were observed at different oxygen concentrations. The values of 18ε and 15ε provided vital parameters for the assessment of assimilatory nitrate reduction via the Rayleigh equation approach. The ratios of O and N isotope enrichment factors (18ε:15ε)assimilation ranged from 0.64 ± 0.15 to 0.74 ± 0.18 during nitrate assimilation by Methylobacter sp. YHQ with Nas, which were different from (18ε:15ε)assimilation for assimilatory eukaryotic nitrate reductase (eukNR) from literature data. Thus, N and O isotope fractionation could be useful tools to distinguish eukNR from Nas during nitrate assimilation. Additionally, the rates of CH4 oxidation and nitrate reduction were evaluated with a reaction-based kinetic model, and it quantitatively described the enzymatic reactions of nitrate assimilation. Combining dual N-O isotope analysis with kinetic modeling provides new insights into the microbially driven C-N interactions.Graphical

Wigner Analysis of Operators. Part II: Schrödinger Equations

We study the phase-space concentration of the so-called generalized metaplectic operators whose main examples are Schrödinger equations with bounded perturbations. To reach this goal, we perform a so-called A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {A}}$$\\end{document}-Wigner analysis of the previous equations, as started in Part I, cf. Cordero and Rodino (Appl Comput Harmon Anal 58:85–123, 2022). Namely, the classical Wigner distribution is extended by considering a class of time–frequency representations constructed as images of metaplectic operators acting on symplectic matrices A∈Sp(2d,R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {A}}\\in Sp(2d,\\mathbb {R})$$\\end{document}. Sub-classes of these representations, related to covariant symplectic matrices, reveal to be particularly suited for the time–frequency study of the Schrödinger evolution. This testifies the effectiveness of this approach for such equations, highlighted by the development of a related wave front set. We first study the properties of A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {A}}$$\\end{document}-Wigner representations and related pseudodifferential operators needed for our goal. This approach paves the way to new quantization procedures. As a byproduct, we introduce new quasi-algebras of generalized metaplectic operators containing Schrödinger equations with more general potentials, extending the results contained in the previous works (Cordero et al. in J Math Pures Appl 99(2):219–233, 2013, J Math Phys 55(8):081506, 2014).

Investigating Latent Interaction Effects in Multiple-Group Analysis in the Structural Equation Modeling Framework

This study aims to address a gap in the social and behavioral sciences literature concerning interaction effects between latent factors in multiple-group analysis. By comparing two approaches for estimating latent interactions within multiple-group analysis frameworks using simulation studies and empirical data, we assess their relative merits. Our simulation study results demonstrated the superiority of the Latent Moderated Structural Equations (LMS) approach over the Unconstrained Product Indicator (UPI) method in power and providing more accurate estimates of differences in latent interactions between groups. Utilizing multiple-group analysis on real-world data, we evaluated its efficacy in identifying latent interaction differences between groups. Empirical data analysis did not reveal discrepancies between LMS and UPI in terms of detecting differences in latent interactions between boys and girls, although they indicated varying sizes of differences in interaction effects. The study concludes with recommendations for examining differences in latent interactions and suggests avenues for future research. Our findings aim to deepen the understanding of intricate relationships among variables, group differences, and the moderating effects of latent variables, ultimately facilitating the development of more accurate theoretical models.

Quiescent optical solitons for Fokas–Lenells equation with nonlinear chromatic dispersion and a couple of self-phase modulation structures

The focus of the current paper is on the retrieval of quiescent optical solitons from Fokas–Lenells equation with nonlinear chromatic dispersion and having quadratic–cubic as well as quadratic–cubic–quartic forms of self-phase modulation structures. Two integration algorithms are implemented to carry out to seek such soliton solutions. They are the enhanced Kudryashov’s approach and the projective Riccati equation approach. In this context, both linear temporal evolution and generalized temporal evolution effects are addressed. A full spectrum of quiescent optical solitons is thus recovered.

Two moments preserving sectional approach for an enzymatic coagulation equation

The coagulation process has found extensive applications in monitoring the evolution of aerosol and granule preparation in pharmaceutical sciences, blood clotting in biology, and cheese manufacturing due to the enzymes in the dairy industry. Among these, modeling the cheese manufacturing process is more challenging due to three indistinguishable sub-mechanisms: (a) enzymatic proteolysis, (b) coagulation, and (c) gelation, which occurs during the enzymatic coagulation of milk. The current study focuses on developing a sectional approach based on the cell average technique for monitoring the evolution of enzyme-induced coagulation of paracasein micelles over time. The proposed technique preserves two integral properties, such as total number and total volume in the system. The mathematical formulation of the proposed technique is very simple, easy to code, and has a robust implementation on any uniform and non-uniform grids. Due to the unavailability of the analytical solutions of the number density functions, the validation of the new proposed approach is done by extracting the new series solutions through the modification of the Homotopy perturbation method [Kaur et al., J. Phys. A 52(38), 385201 (2019)] and exact integral moments for several kernels. It has been shown that the new approach not only estimates the first two integral moments accurately but also computes the second-order moment with high precision without any specific measures. Moreover, domains of varying size grids are taken into account to analyze the convergence behavior of the average-size paracasein micelles formed in the system based on the zeroth and first moments.

Comments on “An application of parametric approach for interval differential equation in inventory model for deteriorating items with selling-price-dependent demand”

Comments on “An application of parametric approach for interval differential equation in inventory model for deteriorating items with selling-price-dependent demand”

Deriving Landauer's formula by using the master equation approach

We revisit the problem of two-terminal transport of non-interacting Fermi particles in a mesoscopic device. First, we generalize the transport problem by taking into consideration relaxation processes in contacts (which are characterized by the contact self-thermalization rate γ) and then solve it by using the master equation approach. In the limit the obtained results are shown to reproduce those of the Landauer theory. Thus, the presented analysis proves correspondence between the Landauer and master equation approaches to quantum transport —a problem which has been waiting for a solution for decades.

Methods Used to Estimate Reservoir Pressure Performance: A Review

Reservoir pressure plays a significant role in all reservoir and production engineering studies. It is crucial to characterize petroleum reservoirs: by detecting fluid movement, computing oil in place, and calculating the recovery factor. Knowledge of reservoir pressure is essential for predicting future production rates, optimizing well performance, or planning enhanced oil recovery strategies. However, applying the methods to investigate reservoir pressure performance is challenging because reservoirs are large, complex systems with irregular geometries in subsurface formations with numerous uncertainties and limited information about the reservoir's structure and behavior. Furthermore, many computational techniques, both numerical and analytical, have been utilized to examine reservoir pressure performance. This paper summarizes the concepts and applications of traditional and novel ways to investigate reservoir pressure changes over time. It provides a comprehensive review that assists the reader in recognizing and distinguishing between various techniques for obtaining an accurate description of reservoir pressure behavior during production, such as the reservoir simulation method, material balance equation approach, time-lapse seismic data, and modern artificial intelligence methods. Thus, the central concept of these procedures and a list of the authors' research are discussed.

Efficient Magnetic Forward Modelling for Strongly Magnetized Bodies: An Iterative Integral Equation Approach

Magnetic surveying encounters challenges in high-precision detection and inversion on strongly magnetized bodies. Non-uniform magnetization caused by self-demagnetization and mutual magnetization makes magnetic field calculation using analytical formulas impractical. The previous discrete numerical methods have suffered from computational inefficiency or low accuracy. To resolve this issue, we develop an algorithm to solve the magnetic field integral equation for calculating the magnetization state of high-susceptibility bodies, combining the improved spatial convolution forward approach with the adaptive relaxation iteration method. To address the excessive computational burden in the magnetization field between 3-D voxel arrays of the discrete model, we construct the circular convolution kernel matrix directly when the subsurface space is divided with an equidistant grid, significantly reducing redundant computations. Then, the fast Fourier transform is used to accelerate the forward discrete circular convolution operation. In addition, we derive an iterative computation scheme that adaptively adjusts the relaxation factor based on magnetic field changes to correct the effective magnetization for algorithm convergence. From a pragmatic perspective, equating the cuboid to equal-volume sphere subdivisions is proposed to enhance computational efficiency further by about 50 per cent despite sacrificing slight accuracy. The sphere and spherical shell models validate the algorithm accuracy, efficiency, and convergence. Furthermore, we analyze the characteristics of the mutual magnetization effect among magnetic bodies under different magnetization conditions. Finally, we demonstrate the applicability of the algorithm through a realistic example. The proposed algorithm shows promise for precisely exploring highly magnetized minerals, underground pipelines, and unexploded ordnance.

A Simultaneous Equation Approach to Examining Linkages Between Income Inequality and Environmental Degradation in Lower Middle-Income Economies in ASEAN

A Simultaneous Equation Approach to Examining Linkages Between Income Inequality and Environmental Degradation in Lower Middle-Income Economies in ASEAN

Anomalous and ultraslow diffusion of a particle driven by power-law-correlated and distributed-order noises

We study the generalised Langevin equation (GLE) approach to anomalous diffusion for a harmonic oscillator and a free particle driven by different forms of internal noises, such as power-law-correlated and distributed-order noises that fulfil generalised versions of the fluctuation-dissipation theorem. The mean squared displacement and the normalised displacement correlation function are derived for the different forms of the friction memory kernel. The corresponding overdamped GLEs for these cases are also investigated. It is shown that such models can be used to describe anomalous diffusion in complex media, giving rise to subdiffusion, superdiffusion, ultraslow diffusion, strong anomaly, and other complex diffusive behaviours.

Dynamics of switching optical soliton in fiber with sixth order dispersion and inter modal dispersion

This work pertains to the study of switching soliton in fiber for nonlinear Schrödinger (NLS) equation with the presence of higher order dispersion and inter modal dispersion (IMD). The nonlinear wave in the optical fiber are described by the NLS equation which having the second order, fourth order, fifth order, sixth order dispersion, higher order nonlinearity and IMD. The main goal of the paper is to examine the sixth order dispersion on nonlinear wave in the fiber with the conditions of IMD. Hence, we employ the Bäcklund transformation of the Riccati equation (BTRE) approach to NLS equation and obtain the soliton solution. By the use of soliton solution along with graphical snapshots, we provide the conditions for forming switching solition in optical fiber and also analyze the effect of sixth order dispersion in fiber. The stability of the solution of NLS equation is also addressed.

Strongly Bound Excitons and Anisotropic Linear Absorption in Monolayer Graphullerene.

Graphullerene is a novel two-dimensional carbon allotrope with unique optoelectronic properties. Despite significant experimental characterization and prior density functional theory calculations, unanswered questions remain as to the nature, energy, and intensity of the electronic and optical excitations. Here, we present first-principles calculations of the quasiparticle band structure, neutral excitations, and absorption spectra of monolayer graphullerene and bulk graphullerite, employing the GW-Bethe-Salpeter equation (GW-BSE) approach. We show that strongly bound excitons dominate the absorption spectrum of monolayer graphullerene with binding energies up to 0.8 eV, while graphullerite exhibits less pronounced excitonic effects. Our calculations also reveal a strong linear polarization anisotropy, reflecting the in-plane structural anisotropy from intermolecular coupling between neighboring C60 units. We further show that the presence of Mg atoms, crucial to the synthesis process, induces structural modifications and polarizability effects, resulting in a ∼1 eV quasiparticle gap renormalization and a reduction in the exciton binding energy to ∼0.6 eV.