Solution Of Model Research Articles

Computational Solution and Analysis of Fuzzy Nonlinear HIV Infection Model via New Multistage Fuzzy Variational Iteration Method

Computational Solution and Analysis of Fuzzy Nonlinear HIV Infection Model via New Multistage Fuzzy Variational Iteration Method

Unifying inflationary and reheating solution

The conventional background solution for the evolution of a single canonical inflaton field performs admirably in extreme scenarios such as the slow-roll phase (where the slow-roll parameter is much less than one) and the deep reheating era (where the Hubble parameter is much smaller than the effective mass of the potential and the field oscillates around the minimum of the potential), but fails to accurately depict the dynamics of the Universe around the end of inflation and the initial oscillatory phases. This article proposes a single, unified, model-independent, parametrized analytical solution for such models that bridges the gap between these two extremes, providing a near-accurate comprehensive description of the evolution of the Universe. This novel strategy has the potential to substantially enhance both quantitative and qualitative cosmological observational predictions, and, as a consequence, can further constrain the inflationary models more effectively using future observations.

Research on time-value-oriented business model innovation path in life services enterprises and its impact on customer perceived value

In the era of the digital economy, the acceleration of life pace has induced to a continuous increase in people’s sense of time scarcity. In order to satisfy consumers’ lifestyle changes and immediate needs, life service enterprises have carried out lots of business model innovation activities guided by value of time. However, it is still unclear what the time-value-oriented business model innovation path is and whether it can improve the perceived value of customers. Under such background, this paper aims to construct a time-value-oriented business model innovation path in life services enterprises and to discuss its relationship with customer perceived value. The study indicates that: Firstly, specific innovation paths of enterprises include putting forward the purpose of value of time proposition, designing standardized process based on time-oriented, constantly forming unique core resources such as big data, brand and supply chain, and updating the transaction method combining online and offline, and so on. Secondly, the questionnaire results indicate that time-value oriented business model innovation in four aspects – value proposition, key processes, core resources, and transaction methods – can effectively enhance customer perceived value. Thirdly, there are differences in the matching degree between time-value-oriented business model innovation and customer value perception among different types of enterprises in the life services industry. Among them, the express delivery industry has the highest enhancing degree and customer satisfaction. This is related to the heterogeneous characteristics of industries such as express delivery, transportation, catering, and retail. Overall, this study offers a comprehensive and practical perspective for enterprises to meet customer perceived value demands by presenting business model innovation paths and solutions.

Characterization of polysulfides (Sx2−) in seawater euxinic conditions by electroanalytical methods

Polysulfides (Sx2−) are important reduced sulfur species (RSS) that play a role in numerous environmental processes. A sound analytical method for the measurement of Sx2− in euxinic waters is lacking. In this work, differential pulse voltammetry (DPV) at the Hg electrode was used to measure the presence of Sx2− in a model seawater solution and an euxinic marine lake (Rogoznica Lake - RL Croatia), in which the concentration of RSS, mainly HS−, varies between 100 and 4000 μM. In the DPV, an adsorption phenomenon associated with Sx2− reduction on Hg produces a characteristic current minimum at −1.0 V (vs. Ag/AgCl), the magnitude of which is proportional to the concentration of polysulfidic sulfur.The DPV current minima were recorded in the model solution K2Sx NaCl/NaHCO3 (pH ∼ 8.2) in a concentration range from 10 to 100 μM of polysulfidic sulfur. Total RSS was measured by cyclic voltammetry, and sampled DC voltammetry showed the ratio between HS− and S0 within the Sx2−. Using the same methodology, the presence of Sx2− below the chemocline enriched by photoptrophic sulfur bacteria was measured in the euxinic layer of RL at concentrations of up to 70 μM of polysulfidic sulfur. The results suggest that euxinic RL samples can be considered as polydisperse solutions of S0 or of S-rich compounds that can change their physicochemical properties and speciation during sample manipulation. These changes can be detected by electrochemistry. Atomic force microscopy proved the release of bacterial cellular S0 during the acidification and purging step in the electrochemical measurements, which contributed to the voltammetric RSS signal.

Eclipse-timing study of new hierarchical triple star candidates in the northern continuous viewing zone of TESS

Aims. We compiled a list of more than 3500 eclipsing binaries located in and near the northern continuous viewing zone (NCVZ) of the TESS space telescope that have sufficient TESS photometry to search for additional hidden components in these systems. In addition to discovering their hierarchical nature, we also determined their orbital parameters and analyzed their distributions. Methods. We obtained the TESS light curves of all targets in an automated way by applying convolution-aided differential photometry on the TESS full-frame images from all available sectors up to sector 60. Using a new self-developed Python GUI, we visually confirmed all of these light curves, determined the eclipsing periods of the objects, and calculated their eclipse-timing variations (ETVs). The ETV curves were used in order to search for nonlinear variations that could be attributed to a light travel-time effect (LTTE) or dynamical perturbations caused by additional components in these systems. We preselected 351 such candidates and modeled their ETVs with the analytic formulae of pure LTTE or with a combination of LTTE and dynamical perturbations. Results. We were able to fit a model solution for the ETVs of 135 hierarchical triple candidates, 10 systems of which were known from the literature, and the remaining 125 systems are new discoveries. These systems include some more noteworthy ones, such as five tight triples that are very close to their dynamical stability limit with a period ratio lower than 20, and three newly discovered triply eclipsing triples. We point out that dynamical perturbations occur in GZ Dra, which we found to be a triple, and that the system is one of the most strongly inclined systems known in the literature, with im = 58° ±7°. We also compared the distributions of some orbital parameters from our solutions with those from a previous Kepler sample. Finally, we verified the correlations between the available parameters for systems that have Gaia non-single star orbital solutions with those from our ETV solutions.

A Parameter Optimization Design and Numerical Calculation Method for Circular Heliostat Field

Solar energy is a low-carbon, eco-friendly, clean energy source that is easily converted into heat and electricity, making the study of solar thermal power generation technology of great significance and with broad application prospects. To improve the performance of solar power plants, it is necessary to reasonably arrange the light reflectors. Both denser heliostats are needed to ensure enough light can be concentrated into the solar collector, thereby improving the power of the power station; at the same time, waste of material must be prevented, striving to increase output thermal power per unit mirror area. This paper is based on the background of the 2023 CUMCM Problem A. Firstly, it analyzes parameters such as the optical efficiency of the original heliostat field, the annual average output power, and the annual average thermal power output per unit mirror area. Secondly, based on the data provided in the appendix, it analyzes the distribution pattern of the heliostat field and establishes an optimization design model for the heliostat field. Next, the optimization design model of the heliostat field is solved using discrete numerical calculation methods. Finally, according to the results of the model solution, the placement positions of the heliostats, the size of the mirrors, and the installation height are adjusted to improve the annual average thermal power output per unit mirror area, thereby achieving an optimized design of the heliostat field.

Investigating the cost of mechanized unpaved road maintenance operations in Uganda

Force Account Mechanism (FAM) is the predominant road maintenance system in Uganda’s local government setup and a similar, though slightly different approach, is used in some large private sector agriculture plantations. With the Uganda Road Fund (URF) 2021/2022 annual report and previous research citing challenges in cost management and efficiency of the FAM method of road maintenance, it becomes paramount to analyse how FAM is implemented in government-led operations, in comparison to similar private sector approaches, while proposing possible solutions to these challenges. This research offered to analyse unpaved road maintenance cost drivers alongside providing a cost model solution to improve on cost prediction of the FAM system. Gulu District Local Government (DLG) and Kakira Sugar Limited (KSL) were selected as case study areas. Two descriptive research methods were used: observations and case study approach. The selected case study areas were accessible and reachable in terms of data. Control parameters affecting unpaved mechanized road maintenance were identified as machine repair costs, tool costs, labour costs, material costs, fuel costs and machine fuel costs. Unpaved mechanized road maintenance costs at KSL and Gulu DLG were computed as a cost/km ratio of 26,442,032Ugx/km (6,958.4USD/km) and 32,674,895Ugx/km (8,598.65USD/km) respectively. The Uganda National Roads Authority (UNRA) unpaved road maintenance costs were calculated as an average of 34,987,122.9Ugx/km (9,165USD/km) while the World Bank ROCKS database provided a comparable figure of 7,971USD/km (30,553,440.83Ugx/km). A USD to Ugx conversion rate of 3,800 was used. Two linear regression cost models with a 0.679 and 0.687 R2 value were computed, and these can be used in preliminary road maintenance cost prediction. The study recommends the need for an effective, digital road maintenance cost database system for mechanized unpaved road maintenance works, cost driver analytics and management, alongside improvement in aspects of maintenance processes at both the DLG and KSL. Further research can be conducted on equipment condition level prediction and analytics in the private sector and at the DLG.

Computational Modeling of Sodium Fluorescein Disposition in Ex Vivo, Machine-Perfused Livers with Ischemia-Reperfusion Injury

Rationale: Quantitation of bile formation machinery activity through biliary sodium fluorescein (SF) clearance is useful for assessing liver viability. Studies have shown that the bile-to-plasma SF ratio is inversely correlated with warm ischemia time (WIT) in rats, which is associated with ischemia-reperfusion injury (IRI)-induced intracellular internalization of the multidrug resistance protein 2 (MRP2) transporter (doi: 10.1152/ajpgi.00038.2022). Computational modeling studies by Monti et al. have demonstrated the sensitivity of biliary SF clearance to MRP2 transporter activity in vivo (doi: 10.48550/arXiv.2302.05511). In vivo experimentation is pertinent for establishing physiological variations occurring during IRI, but transplantation often requires a period of ex vivo machine perfusion (MP). The effects of total hepatectomy, WIT, cold ischemia time (CIT), and MP on biliary function remain unclear. We aim to develop a model for quantitative interpretation of biliary SF clearance kinetics in MP livers to estimate parameters descriptive of the dominant processes determining hepatic SF uptake kinetics in MP livers subjected to different periods of WIT. We hypothesize that increasing WIT will lead to a decrease in the maximal transport velocity (Vmax) parameter for MRP2, which is reflective of decreased biliary SF clearance and diminished liver viability. Methods: Using established protocols (doi: 10.3389/frtra.2023.1215182), livers (n = 3-5) were obtained from anesthetized, male, Sprague-Dawley rats and subjected to 0-, 10-, 20-, or 30-min WIT through ligation of the portal vein and hepatic artery. Livers were removed and subjected to 3 hours of CIT on ice. Livers were attached to a custom normothermic MP system, 0.4 mg/kg SF were added to the MP system’s perfusate-containing reservoir, and SF fluorescence measurements in perfusate and bile were obtained and converted to concentration measurements using standard curves. We modified the liver-centric model described in Monti et al. to account for MP by replacing the liver input functions with ordinary differential equations for SF and its conjugate SF glucuronide (SFG) kinetics in the MP system’s reservoir. The model also accounts for three liver regions (sinusoid, hepatocytes, bile) and major processes, including hepatic transporter kinetics and SF metabolism into SFG, which govern SF dynamics in different model regions. We fit the model solutions using a pseudo-Monte Carlo parameter estimation strategy to each of the datasets by allowing the Vmax parameters to vary, while others were fixed to physiologic values. Results: Time course data for IRI conditions showed a modest decrease in biliary SF with 10- and 20-min WIT and a marked change in biliary SF kinetics with 30-min WIT when compared to control. The MP model was fit to each dataset individually and the model was able to provide a good fit to each dataset. Comparison of Vmax parameters estimated from fitting showed a decrease in MRP2’s Vmax with increasing WIT relative to control. Sensitivity analysis supported our finding by demonstrating that MRP2’s Vmax­ was the most sensitive model parameter. Conclusions: We modified an existing in vivo biliary SF clearance model to account for MP livers and fit the new model to biliary SF clearance data for ex vivo MP livers with varying amounts of WIT. We found that the new model was able to fit biliary SF clearance data for ex vivo MP livers and that the Vmax for MRP2 decreased during MP with increasing WIT. Funded in part by 1F30AI179084-01 to C.M. and NSF DMS 2153387 to R.D. This is the full abstract presented at the American Physiology Summit 2024 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

Solusi Numerik Model Matematika SIPAS dalam Penyebaran Praktik Monkey Business dengan Metode Adams-Bashforth-Moulton

This research is applied research to determine the numerical solution for the SIPAS mathematical model for the spread of monkey business practices using the Adams-Bashforth-Moulton method. The epidemic model for the spread of monkey business practices is susceptible, infected, practiced, and awareness (SIPAS). The discussion begins by determining the initial solution using the fifth order Runge-Kutta method, prediction and correction values using the Adams-Bashforth-Moulton method, simulation and analysis of the results. In this research, it was found that the Adams-Bashforth- Moulton method predicts an increase in the population who know a viral business and become vulnerable(S) due to the number of residents who know a viral business and the population who are aware of the dangers of monkey business practices. Meanwhile, the population that is interested (I), practiced (P) and awareness (A), on the other hand, has decreased and disappeared completely due to a population that has stopped following a viral business and is aware of the dangers of monkey business practices. After carrying out simulations and analyzing the results, it can be seen that the Adams-Bashforth-Moulton method can be used to determine the numerical solution for the SIPAS mathematical model for the spread of monkey business practices.

Determining rational parameters for the treatment of concentrated wastewater from etching site by using combined systems producing sediments of predefined composition

The object of this study is model solutions, spent sulfuric acid and chloride acid etching solutions, degreasing of metal products at enterprises. The paper reports results of research on the possibility of obtaining sediments of predefined composition and reducing the consumption of chemical reagents in comparison with conventional cleaning schemes. The systematization of the elements of the technological scheme has been shown, which provides for the treatment of concentrated wastewater of the etching area in combined systems with obtaining sediments of predefined composition and is the basis for the implementation of resource-saving technology. Rational parameters were established for the state (рН=3‒4, Eh=+0.3‒+0.33 V, and rH2=16.3–19.38 V) and technological parameters (degree of iron extraction ψ=0.8, reagent consumption from the stoichiometric norm of B=0.8). Such parameters provide the proper conditions for the oxidation of organic compounds and their co-precipitation with insoluble iron hydroxy compounds (the maximum degree of extraction of organic impurities is 86 %). The formed precipitate corresponds to the FeOOH.nH2O composition, contains 2‒3 % of organic impurities, and is subject to burial. As a result of studies on the treatment of concentrated iron-containing wastewater, the obtained sediment is ready for further utilization by processing. The composition of this sediment corresponds to the natural mineral limonite FeOOH (Fe2O3.nH2O) and is formed at pH values from 3.5 to 7.5 with rH2 values from 26 V to 21 V and at technological regeneration parameters of pH=4.0–4.6; rH2 =23.34–32.25 V. As a result of research into the deep purification of wastewater using a magnetic device, a suspension of sediment of ferromagnetic impurities (hydroxo compounds of iron) is obtained, which could be the basis for extraction or production of magnetically favorable dispersed material.

Dynamical behaviors of an impulsive stochastic neural field lattice model

This paper is concerned with the asymptotic behaviors of the solutions of an impulsive stochastic neural field lattice model driven by nonlinear noise. We first show the existence and uniqueness of weak pullback mean random attractors for the impulsive stochastic systems. Then by the properties of Markov processes, the existence of evolution system of measures for the impulsive stochastic systems is established. To this end, we employ the idea of uniform estimates on the tails of the solutions to show the tightness of a family of distributions of the solutions of the lattice systems.

A stochastic scale conjugate neural network procedure for the SIRC epidemic delay differential system

In this study, a stochastic computing structure is provided for the numerical solutions of the SIRC epidemic delay differential model, i.e. SIRC-EDDM using the dynamics of the COVID-19. The design of the scale conjugate gradient (CG) neural networks (SCGNNs) is presented for the numerical treatment of SIRC-EDDM. The mathematical model is divided into susceptible S ( ρ ) , recovered R ( ρ ) , infected I ( ρ ) , and cross-immune C ( ρ ) , while the numerical performances have been provided into three different cases. The exactitude of the SCGNNs is perceived through the comparison of the accomplished and reference outcomes (Runge-Kutta scheme) and the negligible absolute error (AE) that are performed around 10−06 to 10−08 for each case of the SIRC-EDDM. The obtained results have been presented to reduce the mean square error (MSE) using the performances of train, validation, and test data. The neuron analysis is also performed that shows the AE by taking 14 neurons provide more accurateness as compared to 4 numbers of neurons. To check the proficiency of SCGNNs, the comprehensive studies are accessible using the error histograms (EHs) investigations, state transitions (STs) values, MSE performances, regression measures, and correlation.

Asymptotic Behavior of Global Solution of an Anomalous Gray Scott Model

The object of this paper is to prove that existence global and asymptotic behavior of solutions for anomalous coupled reaction diffusion system (Gray Scott model) with homogeneous Neumann boundary conditions. The existence and uniqueness of the local solution are given by the Banach fixed point theorem. However, the asymptotic behavior is investiged by technique semi group estimates and the Sobolev embedding theorem

Analytical solution of a gradient-enhanced damage model for quasi-brittle failure

This paper presents an approach for analytically solving gradient-enhanced damage (GED) models. The proposed approach provides rigorous proofs for essential phenomena observed in the traditional GED model, including damage widening, characteristic length sensitivity, and stress-locking. The derived cohesive law is a useful technique for accurately determining the material parameters of the GED model, significantly reducing the sensitivity to characteristic length. Furthermore, this study presents an isotropic damage model that considers both tensile and shear failures and can capture complex crack paths. Finally, a series of numerical examples is shown to demonstrate the efficacy of the suggested method.

From minimal strings towards Jackiw–Teitelboim gravity: on their resurgence, resonance, and black holes

Abstract Two remarkable facts about Jackiw–Teitelboim (JT) two-dimensional dilaton-gravity have been recently uncovered: this theory is dual to an ensemble of quantum mechanical theories; and such ensembles are described by a random matrix model which itself may be regarded as a special (large matter-central-charge) limit of minimal string theory. This work addresses this limit, putting it in its broader matrix-model context; comparing results between multicritical models and minimal strings (i.e. changing in-between multicritical and conformal backgrounds); and in both cases making the limit of large matter-central-charge precise (as such limit can also be defined for the multicritical series). These analyses are first done via spectral geometry, at both perturbative and nonperturbative levels, addressing the resurgent large-order growth of perturbation theory, alongside a calculation of nonperturbative instanton-actions and corresponding Stokes data. This calculation requires an algorithm to reach large-order, which is valid for arbitrary two-dimensional topological gravity. String equations—as derived from the Gel’fand–Dikii construction of the resolvent—are analyzed in both multicritical and minimal string theoretic contexts, and studied both perturbatively and nonperturbatively (always matching against the earlier spectral-geometry computations). The resulting solutions, as described by resurgent transseries, are shown to be resonant. The large matter-central-charge limit is addressed—in the string-equation context—and, in particular, the string equation for JT gravity is obtained to next derivative-orders, beyond the known genus-zero case (its possible exact-form is also discussed). Finally, a discussion of gravitational perturbations to Schwarzschild-like black hole solutions in these minimal-string models, regarded as deformations of JT gravity, is included—alongside a brief discussion of quasinormal modes.

Cauchy hyper-graph Laplacian nonnegative matrix factorization for single-cell RNA-sequencing data analysis.

Many important biological facts have been found as single-cell RNA sequencing (scRNA-seq) technology has advanced. With the use of this technology, it is now possible to investigate the connections among individual cells, genes, and illnesses. For the analysis of single-cell data, clustering is frequently used. Nevertheless, biological data usually contain a large amount of noise data, and traditional clustering methods are sensitive to noise. However, acquiring higher-order spatial information from the data alone is insufficient. As a result, getting trustworthy clustering findings is challenging. We propose the Cauchy hyper-graph Laplacian non-negative matrix factorization (CHLNMF) as a unique approach to address these issues. In CHLNMF, we replace the measurement based on Euclidean distance in the conventional non-negative matrix factorization (NMF), which can lessen the influence of noise, with the Cauchy loss function (CLF). The model also incorporates the hyper-graph constraint, which takes into account the high-order link among the samples. The CHLNMF model's best solution is then discovered using a half-quadratic optimization approach. Finally, using seven scRNA-seq datasets, we contrast the CHLNMF technique with the other nine top methods. The validity of our technique was established by analysis of the experimental outcomes.

Single porosity model: Exploring the spatial resolution limits in complex urban patterns

When modeling large-scale urban floods, the Porosity Nonlinear Shallow Water Equations (PNSWE) emerge as an interesting and consistent subgrid approach to reduce computational time while preserving the solution structure, allowing for computational efficiency at the cost of some loss in the accuracy of the results. Porosity accounts for changes in storage and exchanges due to obstacles in urban areas, and it introduces an extra source term proportional to the porosity gradient into the momentum equations. However, no systematic analyses on the effects of grid size have been performed in real domains, when this model is used to represent fine-scale topographic information at a coarser scale. In this study, we analyze how accuracy is affected by gradually increasing grid resolution in a generalized porosity approach computed at the cell-level. The Single Porosity model (SP) in Cartesian coordinates is employed to simulate a real-world urban flooding event, with resolution transitioning from fine- to macro-scale. At an intermediate scale, the meso-scale, where cell size approximates street width and computational time is significantly reduced, the model captures main preferential flow paths by means of the porosity gradient within the urban area. Good agreement with refined classical model solutions is observed at this scale for flood extension and hazard maps, providing valuable information for early-warning systems. Numerical results underscore the importance of porosity models in rapidly assessing flow properties during an event, enhancing real-time decision-making with reliable information.

Dynamics of Cosmological Scalar Fields Revisited

This paper reviews the dynamics of a single isotropic and homogeneous scalar field φ(t) in the context of cosmological models. A non-standard approach to the solution of the Einstein–Klein–Gordon equations is described which uses the scalar field as the evolution parameter for cosmic dynamics. General conclusions about the qualitative behaviour of the solutions can be drawn, and examples of how to obtain explicit solutions for some cosmological models of interest are given. For arbitrary potentials, analytical results can be obtained from the slow-roll approximation by using a series expansion for the Hubble parameter H[φ], from which a quantitative estimate for the number of e-folds of expansion is obtained. This approach is illustrated with the examples of quadratic potentials and hilltop models, with special consideration of Higgs-type potentials. The GUT-scale is shown to come out of such a model quite naturally. Finally, it is discussed how to find scalar potentials giving rise to a predetermined scalar-field behaviour and the associated evolution of the scale factor.

Intrinsic and Extrinsic Scattering and Absorption Coefficients New Equations in Four-flux and Two-flux Models Used for Determining Light Intensity Gradients

Collimated, diffuse and total light intensity gradients, for forward and backward light senses, were determined in a three substrate layers – glass/electrolyte/glass – almost transparent sample, using optical constants and new equations for intrinsic and extrinsic scattering and absorption coefficients. These new equations were obtained for the inner electrolyte layer from the systems of differential equations of the four-flux and two-flux radiative transfer models, used for determining intrinsic and extrinsic coefficients, respectively, once knowing the optical constants of outer glass layers, from a single glass substrate sample measured in advance. Extinction coefficients were determined from optical constants and considering the wavelength compression of light when it enters into a material, decreasing its speed with respect to the vacuum. The same extinction coefficients for glass and electrolyte layers were computed in three different ways. First, from optical constants, determined using collimated transmittance and reflectance solutions of four-flux model. From them and as intermediate parameters for glass and electrolyte layers, collimated interface reflectance and attenuation due to extinction were computed since they were required for determining inner collimated light intensities at the interfaces, which were used at the collimated forward and backward differential equations, solving for the forward and backward extinction coefficients. The three-extinction matching requirement was successfully satisfied for the glass and electrolyte layers. Two average crossing parameters equations, for each sense, and four forward scattering ratios equations, for collimated and for diffuse light intensities for each sense, were used in the system of diffuse differential equations for intrinsic coefficients. For them, intuitive equations were proposed, based on collimated and diffuse light intensities at each interface. New equations for extrinsic parameters were determined by equalizing the system of total differential equations of the two-flux model to the sum of the systems of collimated and diffuse differential equations of the four-flux model.

Iterative MILP algorithm to find alternate solutions in linear programming models

AbstractWe address in this paper linear programming (LP) models in which it is desired to find a finite set of alternate optima. An LP may have multiple alternate solutions with the same objective value or with increasing objective values. For many real life applications, it can be interesting to have a pool of solutions to compare what operations should be executed and what is the cost/benefit of doing it. To obtain a specified number of these alternate solutions in the increasing order of objective values, we propose an iterative MILP algorithm in which we successively add integer cuts on inactive constraints. We demonstrate the application and effectiveness of this algorithm on a 2 dimensional LP and on small and large supply chain problems. The proposed iterative MILP algorithm provides an effective approach for finding a specified number of alternate optima in LP models, which provides a useful tool in a variety of applications as for instance in supply chain optimization problems.