Search results for: generalized mathematical model

Authors: M. O. Olayiwola

Abstract:

Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: Nisa Özge Önal, Kamil Karaçuha, Göksu Hazar Erdinç, Banu Bahar Karaçuha, Ertuğrul Karaçuha

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The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.

Keywords: children growth percentile, children physical development, fractional calculus, linear and polynomial model

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Authors: Fuad Al Sarari

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The purpose of the present paper is to study subclasses of analytic functions which generalize the classes of Janowski functions introduced by Polatoglu. We study certain convolution conditions. This leads to a study of the sufficient condition and the neighborhood results related to the functions in the class S (T; H; F ): and a study of new subclasses of analytic functions that are defined using notions of the generalized Janowski classes and -symmetrical functions. In the quotient of analytical representations of starlikeness and convexity with respect to symmetric points, certain inherent properties are pointed out.

Keywords: convolution conditions, subordination, Janowski functions, starlike functions, convex functions

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Authors: Aya Al Masri, Stefaan Carpentier, Fabrice Leroy, Thibault Julien, Safoin Aktaou, Malorie Martin, Fouad Maaloul

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Introduction: During an 'Interventional Radiology (IR)' procedure, the patient's skin-dose may become very high for a burn, necrosis and ulceration to appear. In order to prevent these deterministic effects, an accurate calculation of the patient skin-dose mapping is essential. For most machines, the 'Dose Area Product (DAP)' and fluoroscopy time are the only information available for the operator. These two parameters are a very poor indicator of the peak skin dose. We developed a mathematical model that reconstructs the magnitude (delivered dose), shape, and localization of each irradiation field on the patient skin. In case of critical dose exceeding, the system generates warning alerts. We present the results of its comparison with clinical studies. Materials and methods: Two series of comparison of the skin-dose mapping of our mathematical model with clinical studies were performed: 1. At a first time, clinical tests were performed on patient phantoms. Gafchromic films were placed on the table of the IR machine under of PMMA plates (thickness = 20 cm) that simulate the patient. After irradiation, the film darkening is proportional to the radiation dose received by the patient's back and reflects the shape of the X-ray field. After film scanning and analysis, the exact dose value can be obtained at each point of the mapping. Four experimentation were performed, constituting a total of 34 acquisition incidences including all possible exposure configurations. 2. At a second time, clinical trials were launched on real patients during real 'Chronic Total Occlusion (CTO)' procedures for a total of 80 cases. Gafchromic films were placed at the back of patients. We performed comparisons on the dose values, as well as the distribution, and the shape of irradiation fields between the skin dose mapping of our mathematical model and Gafchromic films. Results: The comparison between the dose values shows a difference less than 15%. Moreover, our model shows a very good geometric accuracy: all fields have the same shape, size and location (uncertainty < 5%). Conclusion: This study shows that our model is a reliable tool to warn physicians when a high radiation dose is reached. Thus, deterministic effects can be avoided.

Keywords: clinical experimentation, interventional radiology, mathematical model, patient's skin-dose mapping.

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Authors: Elisa Boatti, Ulisse Stefanelli, Alessandro Reali, Ferdinando Auricchio

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Thanks to their unusual properties, shape memory alloys (SMAs) are good candidates for advanced applications in a wide range of engineering fields, such as automotive, robotics, civil, biomedical, aerospace. In the last decades, the ever-growing interest for such materials has boosted several research studies aimed at modeling their complex nonlinear behavior in an effective and robust way. Since the constitutive response of SMAs is strongly thermomechanically coupled, the investigation of the non-isothermal evolution of the material must be taken into consideration. The present study considers an existing three-dimensional phenomenological model for SMAs, able to reproduce the main SMA properties while maintaining a simple user-friendly structure, and proposes a variational reformulation of the full non-isothermal version of the model. While the considered model has been thoroughly assessed in an isothermal setting, the proposed formulation allows to take into account the full nonisothermal problem. In particular, the reformulation is inspired to the GENERIC (General Equations for Non-Equilibrium Reversible-Irreversible Coupling) formalism, and is based on a generalized gradient flow of the total entropy, related to thermal and mechanical variables. Such phrasing of the model is new and allows for a discussion of the model from both a theoretical and a numerical point of view. Moreover, it directly implies the dissipativity of the flow. A semi-implicit time-discrete scheme is also presented for the fully coupled thermomechanical system, and is proven unconditionally stable and convergent. The correspondent algorithm is then implemented, under a space-homogeneous temperature field assumption, and tested under different conditions. The core of the algorithm is composed of a mechanical subproblem and a thermal subproblem. The iterative scheme is solved by a generalized Newton method. Numerous uniaxial and biaxial tests are reported to assess the performance of the model and algorithm, including variable imposed strain, strain rate, heat exchange properties, and external temperature. In particular, the heat exchange with the environment is the only source of rate-dependency in the model. The reported curves clearly display the interdependence between phase transformation strain and material temperature. The full thermomechanical coupling allows to reproduce the exothermic and endothermic effects during respectively forward and backward phase transformation. The numerical tests have thus demonstrated that the model can appropriately reproduce the coupled SMA behavior in different loading conditions and rates. Moreover, the algorithm has proved effective and robust. Further developments are being considered, such as the extension of the formulation to the finite-strain setting and the study of the boundary value problem.

Keywords: generalized gradient flow, GENERIC formalism, shape memory alloys, thermomechanical coupling

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Authors: Mike Tsionas

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The paper develops new indices of financial stability based on an explicit model of expected utility maximization by financial institutions subject to the classical technology restrictions of neoclassical production theory. The model can be estimated using standard econometric techniques, like GMM for dynamic panel data and latent factor analysis for the estimation of co-variance matrices. An explicit functional form for the utility function is not needed and we show how measures of risk aversion and prudence (downside risk aversion) can be derived and estimated from the model. The model is estimated using data for Eurozone countries and we focus particularly on (i) the use of the modeling approach as an “early warning mechanism”, (ii) the bank- and country-specific estimates of risk aversion and prudence (downside risk aversion), and (iii) the derivation of a generalized measure of risk that relies on loan-price uncertainty.

Keywords: financial stability, banking, expected utility maximization, sub-prime crisis, financial crisis, eurozone, PIIGS

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Authors: Mahtab Baghaei, Seyed Mahmoud Tabatabaei

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Aim & Background: Electrical stimulation of transcranial direct current is considered one of the treatment methods for mental disorders. The aim of this study was to evaluate the effectiveness of transcranial electrical stimulation on the delta, theta, alpha, beta and systolic and diastolic blood pressure in patients with generalized anxiety disorder. Materials and Methods: The present study was a double-blind intervention with a pre-test and post-test design on people with generalized anxiety disorder in Tabriz in 1400. In this study, 30 patients with generalized anxiety disorder were selected by purposive sampling method based on the criteria specified in DSM-5 and randomly divided into an experimental group (n = 15) and a control group (n = 15). The experimental group received two sessions of 30 minutes of electrical stimulation of transcranial direct current with an intensity of 2 mA in the area of the lateral dorsal prefrontal cortex, and the control group also received artificial stimulation. Results: The results showed that transcranial electrical stimulation reduces delta and theta waves and increases beta and alpha brain waves in the experimental group. On the other hand, this method also showed a significant decrease in systolic and diastolic blood pressure in these patients (p <0.01). Conclusion: The results show that transcranial electrical stimulation has a statistically significant effect on brain waves and blood pressure, and this non-invasive method can be used as one of the treatment methods in people with generalized anxiety disorder.

Keywords: transcranial direct current electrical stimulation, brain waves, systolic blood pressure, diastolic blood pressure

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Authors: Asrat M.Belachew, Tiago Pereira, Institute of Mathematics, Computer Sciences, Avenida Trabalhador São Carlense, 400, São Carlos, 13566-590, Brazil

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Infectious diseases are among the most prominent threats to human beings. They cause morbidity and mortality to an individual and collapse the social, economic, and political systems of the whole world collectively. Mathematical models are fundamental tools and provide a comprehensive understanding of how infectious diseases spread and designing the control strategy to mitigate infectious diseases from the host population. Modeling the spread of infectious diseases using a compartmental model of inhomogeneous populations is good in terms of complexity. However, in the real world, there is a situation that accounts for heterogeneity, such as ages, locations, and contact patterns of the population which are ignored in a homogeneous setting. In this work, we study how classical an SEIR infectious disease spreading of the compartmental model can be extended by incorporating the mobility of population between heterogeneous cities during an outbreak of infectious disease. We have formulated an SEIR multi-cities epidemic spreading model using a system of 4k ordinary differential equations to describe the disease transmission dynamics in k-cities during the day and night. We have shownthat the model is epidemiologically (i.e., variables have biological interpretation) and mathematically (i.e., a unique bounded solution exists all the time) well-posed. We constructed the next-generation matrix (NGM) for the model and calculated the basic reproduction number R0for SEIR-epidemic spreading model with cities mobility. R0of the disease depends on the spectral radius mobility operator, and it is a threshold between asymptotic stability of the disease-free equilibrium and disease persistence. Using the eigenvalue perturbation theorem, we showed that sending a fraction of the population between cities decreases the reproduction number of diseases in interconnected cities. As a result, disease transmissiondecreases in the population.

Keywords: SEIR-model, mathematical model, city mobility, epidemic spreading

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Authors: Roslinda Nazar, Ezad Hafidz Hafidzuddin, Norihan M. Arifin, Ioan Pop

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In this paper, the problem of steady laminar boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity is considered. The similarity transformations are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations. The transformed equations are then solved numerically using the bvp4c function in MATLAB. Dual solutions are found for a certain range of the suction and stretching/shrinking parameters. The effects of the suction parameter, stretching/shrinking parameter, velocity slip parameter, critical shear rate, and Prandtl number on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented and discussed.

Keywords: boundary layer, exponentially stretching/shrinking sheet, generalized slip, heat transfer, numerical solutions

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Authors: Jiahui Song

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In order to predict or explain a complicated biological process, it is important first to construct mathematical models that can be used to yield analytical solutions. Through numerical simulation, mathematical model results can be used to test scenarios that might not be easily attained in a laboratory experiment, or to predict parameters or phenomena. High-intensity, nanosecond pulse electroporation has been a recent development in bioelectrics. The dynamic pore model can be achieved by including a dynamic aspect and a dependence on the pore population density into pore formation energy equation to analyze and predict such electroporation effects. For greater accuracy, with inclusion of atomistic details, molecular dynamics (MD) simulations were also carried out during this study. Besides inducing pores in cells, external voltages could also be used in principle to modulate action potential generation in nerves. This could have an application in electrically controlled ‘pain management’. Also a simple model-based rate equation treatment of the various cellular bio-chemical processes has been used to predict the pulse number dependent cell survival trends.

Keywords: model, high-intensity, nanosecond, bioelectrics

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Authors: Qian Zhang, Dongkai Shen, Yan Shi

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A new mechanical ventilator with automatic secretion clearance function can improve the secretion clearance safely and efficiently. However, in recent modeling studies on various mechanical ventilators, it was considered that human had one lung, and the coupling effect of double lungs was never illustrated. In this paper, to expound the coupling effect of double lungs, a mathematical model of a ventilation system of a bi-level positive airway pressure (BiPAP) controlled ventilator with secretion clearance was set up. Moreover, an experimental study about the mechanical ventilation system of double lungs on BiPAP ventilator was conducted to verify the mathematical model. Finally, the coupling effect of double lungs of the mathematical ventilation was studied by simulation and orthogonal experimental design. This paper adds to previous studies and can be referred to optimization methods in medical researches.

Keywords: double lungs, coupling effect, secretion clearance, orthogonal experimental design

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Authors: F. Calderón-Vega, A. D. García-Soto, C. Mösso

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Recorded significant wave heights sometimes exhibit large uncommon values (outliers) that can be associated with extreme phenomena such as hurricanes and cold fronts. In this study, some extremely large wave heights recorded in NOAA buoys (National Data Buoy Center, noaa.gov) are used to investigate their effect in the prediction of future wave heights associated with given return periods. Extreme waves are predicted through a time-dependent model based on the so-called generalized extreme value distribution. It is found that the outliers do affect the estimated wave heights. It is concluded that a detailed inspection of outliers is envisaged to determine whether they are real recorded values since this will impact defining design wave heights for coastal protection purposes.

Keywords: GEV model, non-stationary, seasonality, outliers

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Authors: Linda A. O’Higgins, Astrid Wingler, Jorge Oliveira

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The growth of Chlorella vulgaris was characterized as a function of irradiance in a laboratory turbidostat (1 L) and compared to batch growth in sunlit modules (5–25 L) of the commercial Phytobag photobioreactor. The effects of variable sunlight and culture density were deconvoluted by a mathematical model. The analysis showed that algal growth was light-limited due to shading by external construction elements and due to light attenuation within the algal bags. The model was also used to predict maximum biomass productivity. The manipulative experiments and the model predictions were confronted with data from a production season of a 10m2 pilot-scale photobioreactor, Phytobag (10,000 L). The analysis confirmed light limitation in all three photobioreactors. An additional limitation of biomass productivity was caused by the nitrogen starvation that was used to induce lipid accumulation. Reduction of shading and separation of biomass and lipid production are proposed for future optimization.

Keywords: microalgae, batch cultivation, Chlorella vulgaris, Mathematical model, photobioreactor, scale-up

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Authors: Tai-Yue Wang, Yi-Ho Chen

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In this study, we investigate a two-echelon supply chain with two suppliers and three retailers among which one retailer dominates other retailers. A price competition demand function is used to model this dominant retailer, which is leading market. The promotion strategies and negotiation schemes are integrated to form decision-making models under different scenarios. These models are then formulated into different mathematical programming models. The decision variables such as promotional costs, retailer prices, wholesale price, and order quantity are included in these models. At last, the distributions of promotion costs under different cost allocation strategies are discussed. Finally, an empirical example used to validate our models. The results from this empirical example show that the profit model will create the largest profit for the supply chain but with different profit-sharing results. At the same time, the more risk a member can take, the more profits are distributed to that member in the utility model.

Keywords: supply chain, price promotion, mathematical models, dominant retailer

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Authors: Cihan Çetinkaya, Eren Özceylan, Kerem Elibal

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This paper presents a solution method for selection of production facility. The motivation has been taken from a real life case, an automotive subcontractor which has two production facilities at different cities and parts. The problem is to decide which part(s) should be produced at which facility. To the best of our knowledge, until this study, there was no scientific approach about this problem at the firm and decisions were being given intuitively. In this study, some logistic cost parameters have been defined and with these parameters a mathematical model has been constructed. Defined and collected cost parameters are handling cost of parts, shipment cost of parts and shipment cost of welding fixtures. Constructed multi-objective mathematical model aims to minimize these costs while aims to balance the workload between two locations. Results showed that defined model can give optimum solutions in reasonable computing times. Also, this result gave encouragement to develop the model with addition of new logistic cost parameters.

Keywords: automotive subcontract, facility assignment, logistic costs, multi-objective models

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Authors: Ella Tyuryumina, Alexey Neznanov

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Finding algorithms to predict the growth of tumors has piqued the interest of researchers ever since the early days of cancer research. A number of studies were carried out as an attempt to obtain reliable data on the natural history of breast cancer growth. Mathematical modeling can play a very important role in the prognosis of tumor process of breast cancer. However, mathematical models describe primary tumor growth and metastases growth separately. Consequently, we propose a mathematical growth model for primary tumor and primary metastases which may help to improve predicting accuracy of breast cancer progression using an original mathematical model referred to CoM-IV and corresponding software. We are interested in: 1) modelling the whole natural history of primary tumor and primary metastases; 2) developing adequate and precise CoM-IV which reflects relations between PT and MTS; 3) analyzing the CoM-IV scope of application; 4) implementing the model as a software tool. The CoM-IV is based on exponential tumor growth model and consists of a system of determinate nonlinear and linear equations; corresponds to TNM classification. It allows to calculate different growth periods of primary tumor and primary metastases: 1) ‘non-visible period’ for primary tumor; 2) ‘non-visible period’ for primary metastases; 3) ‘visible period’ for primary metastases. The new predictive tool: 1) is a solid foundation to develop future studies of breast cancer models; 2) does not require any expensive diagnostic tests; 3) is the first predictor which makes forecast using only current patient data, the others are based on the additional statistical data. Thus, the CoM-IV model and predictive software: a) detect different growth periods of primary tumor and primary metastases; b) make forecast of the period of primary metastases appearance; c) have higher average prediction accuracy than the other tools; d) can improve forecasts on survival of BC and facilitate optimization of diagnostic tests. The following are calculated by CoM-IV: the number of doublings for ‘nonvisible’ and ‘visible’ growth period of primary metastases; tumor volume doubling time (days) for ‘nonvisible’ and ‘visible’ growth period of primary metastases. The CoM-IV enables, for the first time, to predict the whole natural history of primary tumor and primary metastases growth on each stage (pT1, pT2, pT3, pT4) relying only on primary tumor sizes. Summarizing: a) CoM-IV describes correctly primary tumor and primary distant metastases growth of IV (T1-4N0-3M1) stage with (N1-3) or without regional metastases in lymph nodes (N0); b) facilitates the understanding of the appearance period and manifestation of primary metastases.

Keywords: breast cancer, exponential growth model, mathematical modelling, primary metastases, primary tumor, survival

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Authors: Androniki-Anna Doulgeroglou, Panagiotis Kotronis, Giulio Sciarra, Catherine Bouillon

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The interaction diagrams are functions that define ultimate states expressed in terms of generalized forces (axial force, bending moment and shear force). Two characteristic states for reinforced concrete (RC) sections are proposed: the first characteristic state corresponds to the yield of the reinforcement bars and the second to the peak values of the generalized forces generalized displacements curves. 3D numerical simulations are then conducted for RC columns and the global responses are compared to experimental results. Interaction diagrams for combined flexion, shear and axial force loading conditions are numerically produced for symmetrically RC square sections for different reinforcement ratios. Analytical expressions of the interaction diagrams are also proposed, satisfying the condition of convexity. Comparison with interaction diagrams from the Eurocode is finally presented for the study cases.

Keywords: analytical convex expressions, finite element method, interaction diagrams, reinforced concrete

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Authors: Hossein Kabir, Amir Hossein Hassanpour Mati-Kolaie

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In the current study, the elastic field in an anisotropic elastic media is determined by implementing a general semi-analytical method. In this specific methodology, the displacement field is computed as a sum of finite functions with unknown coefficients. These aforementioned functions satisfy exactly both the homogeneous and inhomogeneous boundary conditions in the proposed media. It is worth mentioning that the unknown coefficients are determined by implementing the principle of minimum potential energy. The numerical integration is implemented by employing the Generalized Gaussian Quadrature solution. Furthermore, with the aid of the calculated unknown coefficients, the displacement field, as well as the other parameters of the elastic field, are obtainable as well. Finally, the comparison of the previous analytical method with the current semi-analytical method proposes the efficacy of the present methodology.

Keywords: anisotropic elastic media, semi-analytical method, elastic field, generalized gaussian quadrature solution

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Authors: Babak Safaei, Ahmad Ghanbari, Arash Rahmani

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In the present study, the free vibration characteristics of double-walled carbon nanotubes (DWCNTs) are investigated. The small-scale effects are taken into account using the Eringen’s nonlocal elasticity theory. The nonlocal elasticity equations are implemented into the different classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), Reddy beam theory (RBT), and Levinson beam theory (LBT) to analyze the free vibrations of DWCNTs in which each wall of the nanotubes is considered as individual beam with van der Waals interaction forces. Generalized differential quadrature (GDQ) method is utilized to discretize the governing differential equations of each nonlocal beam model along with four commonly used boundary conditions. Then molecular dynamics (MD) simulation is performed for a series of armchair and zigzag DWCNTs with different aspect ratios and boundary conditions, the results of which are matched with those of nonlocal beam models to extract the appropriate values of the nonlocal parameter corresponding to each type of chirality, nonlocal beam model and boundary condition. It is found that the present nonlocal beam models with their proposed correct values of nonlocal parameter have good capability to predict the vibrational behavior of DWCNTs, especially for higher aspect ratios.

Keywords: double-walled carbon nanotubes, nonlocal continuum elasticity, free vibrations, molecular dynamics simulation, generalized differential quadrature method

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Authors: Kayode Oshinubi, Brice Kammegne, Jacques Demongeot

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The use of mathematical tools like Partial Differential Equations and Ordinary Differential Equations have become very important to predict the evolution of a viral disease in a population in order to take preventive and curative measures. In December 2019, a novel variety of Coronavirus (SARS-CoV-2) was identified in Wuhan, Hubei Province, China causing a severe and potentially fatal respiratory syndrome, i.e., COVID-19. Since then, it has become a pandemic declared by World Health Organization (WHO) on March 11, 2020 which has spread around the globe. A reaction-diffusion system is a mathematical model that describes the evolution of a phenomenon subjected to two processes: a reaction process in which different substances are transformed, and a diffusion process that causes a distribution in space. This article provides a mathematical study of the Susceptible, Exposed, Infected, Recovered, and Vaccinated population model of the COVID-19 pandemic by the bias of reaction-diffusion equations. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined using the Lyapunov function are considered and the endemic equilibrium point exists and is stable if it satisfies Routh–Hurwitz criteria. Also, adequate conditions for the existence and uniqueness of the solution of the model have been proved. We showed the spatial distribution of the model compartments when the basic reproduction rate $\mathcal{R}_0 < 1$ and $\mathcal{R}_0 > 1$ and sensitivity analysis is performed in order to determine the most sensitive parameters in the proposed model. We demonstrate the model's effectiveness by performing numerical simulations. We investigate the impact of vaccination and the significance of spatial distribution parameters in the spread of COVID-19. The findings indicate that reducing contact with an infected person and increasing the proportion of susceptible people who receive high-efficacy vaccination will lessen the burden of COVID-19 in the population. To the public health policymakers, we offered a better understanding of the COVID-19 management.

Keywords: COVID-19, SEIRV epidemic model, reaction-diffusion equation, basic reproduction number, vaccination, spatial distribution

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Authors: Paras Ram, Vikas Kumar

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The transmission of Malaria with seasonal were studied through the use of mathematical models. The data from the annual number of Malaria cases reported to the Division of Epidemiology, Ministry of Public Health, Thailand during the period 1997-2011 were analyzed. The transmission of Malaria with seasonal was studied by formulating a mathematical model which had been modified to describe different situations encountered in the transmission of Malaria. In our model, the population was separated into two groups: the human and vector groups, and then constructed a system of nonlinear differential equations. Each human group was divided into susceptible, infectious in hot season, infectious in rainy season, infectious in cool season and recovered classes. The vector population was separated into two classes only: susceptible and infectious vectors. The analysis of the models was given by the standard dynamical modeling.

Keywords: ferrofluid, magnetic field, porous medium, rotating disk, Neuringer-Rosensweig Model

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Authors: Yagya Raj Pandeya, Joonwhoan Lee

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The dynamic behavior of music and video makes it difficult to evaluate musical instrument playing in a video by computer system. Any television or film video clip with music information are rich sources for analyzing musical instruments using modern machine learning technologies. In this research, we integrate the audio and video information sources using convolutional neural network (CNN) and pass network learned features through recurrent neural network (RNN) to preserve the dynamic behaviors of audio and video. We use different pre-trained CNN for music and video feature extraction and then fine tune each model. The music network use 2D convolutional network and video network use 3D convolution (C3D). Finally, we concatenate each music and video feature by preserving the time varying features. The long short term memory (LSTM) network is used for long-term dynamic feature characterization and then use late fusion with generalized mean. The proposed network performs better performance to recognize the musical instrument using audio-video multimodal neural network.

Keywords: multimodal, 3D convolution, music-video feature extraction, generalized mean

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Authors: Ledeza Jordan Babiano

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Translating statements into mathematical notations is one of the processes in word problem-solving. However, based on the literature, students still have difficulties with this skill. The purpose of this study was to investigate the translation errors of the students when they translate algebraic word problems into mathematical structures and locate the errors via the lens of the Translation-Verification Model. Moreover, this qualitative research study employed content analysis. During the data-gathering process, the students were asked to answer a six-item algebra word problem questionnaire, and their answers were analyzed by experts through blind coding using the Translation-Verification Model to determine their translation errors. After this, a focus group discussion was conducted, and the data gathered was analyzed through thematic analysis to determine the causes of the students’ translation errors. It was found out that students’ prevalent error in translation was the interpretation error, which was situated in the Attribute construct. The emerging themes during the FGD were: (1) The procedure of translation is strategically incorrect; (2) Lack of comprehension; (3) Algebra concepts related to difficulty; (4) Lack of spatial skills; (5) Unprepared for independent learning; and (6) The content of the problem is developmentally inappropriate. These themes boiled down to the major concept of independent learning preparedness in solving mathematical problems. This concept has subcomponents, which include contextual and conceptual factors in translation. Consequently, the results provided implications for instructors and professors in Mathematics to innovate their teaching pedagogies and strategies to address translation gaps among students.

Keywords: mathematical structure, algebra word problems, translation, errors

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Authors: Meraj Ali Khan, Falleh R. Al-Solamy

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In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F, b, φ, ρ, θ)− univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F, b, φ, ρ, θ)− univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature.

Keywords: duality, multiobjective programming, univex functions, univex

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Authors: Prajwal Prakash Vasisht, Sharath Rajamurthy, Nishanth Dara

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In a supervised machine learning approach, metrics such as precision, accuracy, and coverage can be calculated using ground truth labels to help in model tuning, evaluation, and selection. In an unsupervised setting, however, where the data has no ground truth, there are few interpretable metrics that can guide us to do the same. Our approach creates a framework to adapt the Intersection over Union metric, referred to as Adapted IoU, usually used to evaluate supervised learning models, into the unsupervised domain, which solves the problem by factoring in subject matter expertise and intuition about the ideal output from the model. This metric essentially provides a scale that allows us to compare the performance across numerous unsupervised models or tune hyper-parameters and compare different versions of the same model.

Keywords: general metric, unsupervised learning, classification, intersection over union

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Authors: Hassan Al Salman

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We consider a nonlinear parabolic cross diffusion model arising in applied mathematics. A fully practical piecewise linear finite element approximation of the model is studied. By using entropy-type inequalities and compactness arguments, existence of a global weak solution is proved. Providing further regularity of the solution of the model, some uniqueness results and error estimates are established. Finally, some numerical experiments are performed.

Keywords: cross diffusion model, entropy-type inequality, finite element approximation, numerical analysis

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Authors: Sergey Podluzhnyy

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One of the most important tasks of investment and pension fund management is building decision support system which helps to make right decision on corporate bond portfolio formation. Today there are several basic methods of bond portfolio management. They are duration management, immunization and convexity management. Identified methods have serious disadvantage: they do not take into account credit risk or insolvency risk of issuer. So, identified methods can be applied only for management and evaluation of high-quality sovereign bonds. Applying article proposes mathematical model for building an optimal in case of risk and yield corporate bond portfolio. Proposed model takes into account the default probability in formula of assessment of bonds which results to more correct evaluation of bonds prices. Moreover, applied model provides tools for visualization of the efficient frontier of corporate bonds portfolio taking into account the exposure to credit risk, which will increase the quality of the investment decisions of portfolio managers.

Keywords: corporate bond portfolio, default probability, effective boundary, portfolio optimization task

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Authors: Manana Chumburidze, David Lekveishvili

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We have considered the harmonic oscillations and general dynamic (pseudo oscillations) systems of theory generalized Green-Lindsay of couple-stress thermo-elasticity for isotropic, homogeneous elastic media. Approximate solution of some mixed boundary value problems for finite domain, bounded by the some closed surface are constructed.

Keywords: the couple-stress thermoelasticity, boundary value problems, dynamic problems, approximate solution

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Authors: Mahbub C. Mishu, Venktesh N. Dubey, Tamas Hickish, Jonathan Cole

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Pressure ulcer is a common problem for today's healthcare industry. It occurs due to external load applied to the skin. Also when the subject is immobile for a longer period of time and there is continuous load applied to a particular area of human body,blood flow gets reduced and as a result pressure ulcer develops. Body support surface has a significant role in preventing ulceration so it is important to know the characteristics of support surface under loading conditions. In this paper we have presented mathematical models of different types of viscoelastic materials and also we have shown the validation of our simulation results with experiments.

Keywords: pressure ulcer, viscoelastic material, mathematical model, experimental validation

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Authors: Jamal Hussain Al-Smail

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Hydrogen fuel cells (HFCs) are environmentally friendly, energy converter devices that convert the chemical energy of the reactants (oxygen and hydrogen) to electricity through electrochemical reactions. The level of the electricity production of HFCs mainly increases depending on the oxygen distribution in the HFC’s cathode gas diffusion layer (GDL). With a constant porosity of the GDL, the electrochemical reaction can have a great variation that reduces the cell’s productivity and stability. Our findings bring a methodology in finding porosity designs of the diffusion layer to improve the oxygen distribution such that it results in a stable oxygen-hydrogen reaction. We first introduce a mathematical model involving the mass and momentum transport equations, in which a porosity function of the GDL is incorporated as a control for the fluid flow. We then derive numerical methods for solving the mathematical model. In conclusion, we present our numerical results to show how to design the GDL porosity to result in a uniform oxygen distribution.

Keywords: fuel cells, material porosity design, mathematical modeling, porous media

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