Search results for: differential constitutive models

Authors: J. P. Chollom, G. M. Kumleng, S. Longwap

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The search for higher order A-stable linear multi-step methods has been the interest of many numerical analysts and has been realized through either higher derivatives of the solution or by inserting additional off step points, supper future points and the likes. These methods are suitable for the solution of stiff differential equations which exhibit characteristics that place a severe restriction on the choice of step size. It becomes necessary that only methods with large regions of absolute stability remain suitable for such equations. In this paper, high order block implicit multi-step methods of the hybrid form up to order twelve have been constructed using the multi-step collocation approach by inserting one or more off step points in the multi-step method. The accuracy and stability properties of the new methods are investigated and are shown to yield A-stable methods, a property desirable of methods suitable for the solution of stiff ODE’s. The new High Order Block Implicit Multistep methods used as block integrators are tested on stiff differential systems and the results reveal that the new methods are efficient and compete favourably with the state of the art Matlab ode23 code.

Keywords: block linear multistep methods, high order, implicit, stiff differential equations

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Authors: Muath Awadalla, Maen Awadallah

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Banking sector covers different activities including lending money to customers. However, it is commonly known that customers pay money they have borrowed including an added amount called interest. Compound interest rate is an approach used in determining the interest to be paid. The instant compounded amount to be paid by a debtor is obtained through a differential equation whose main parameters are the rate and the time. The rate used by banks in a country is often defined by the government of the said country. In Switzerland, for instance, a negative rate was once applied. In this work, a new approach of modeling the compound interest is proposed using Hadamard fractional derivative. As a result, it appears that depending on the fraction value used in derivative the amount to be paid by a debtor might either be higher or lesser than the amount determined using the classical approach.

Keywords: compound interest, fractional differential equation, hadamard fractional derivative, optimization

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Authors: Ramzi B. Albadarneh

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In this paper, we use the new definition of fractional derivative called conformable fractional derivative to derive some finite difference formulas and its error terms which are used to solve fractional differential equations and fractional partial differential equations, also to derive fractional Euler method and its error terms which can be applied to solve fractional differential equations. To provide the contribution of our work some applications on finite difference formulas and Euler Method are given.

Keywords: conformable fractional derivative, finite difference formula, fractional derivative, finite difference formula

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Authors: Velimir "monty" Vesselinov, Trais Kliplhuis, Hope Jasperson

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Artificial intelligence (AI) is a powerful tool in the geothermal energy sector, aiding in both exploration and utilization. Identifying promising geothermal sites can be challenging due to limited surface indicators and the need for expensive drilling to confirm subsurface resources. Geothermal reservoirs can be located deep underground and exhibit complex geological structures, making traditional exploration methods time-consuming and imprecise. AI algorithms can analyze vast datasets of geological, geophysical, and remote sensing data, including satellite imagery, seismic surveys, geochemistry, geology, etc. Machine learning algorithms can identify subtle patterns and relationships within this data, potentially revealing hidden geothermal potential in areas previously overlooked. To address these challenges, a SIML (Science-Informed Machine Learning) technology has been developed. SIML methods are different from traditional ML techniques. In both cases, the ML models are trained to predict the spatial distribution of an output (e.g., pressure, temperature, heat flux) based on a series of inputs (e.g., permeability, porosity, etc.). The traditional ML (a) relies on deep and wide neural networks (NNs) based on simple algebraic mappings to represent complex processes. In contrast, the SIML neurons incorporate complex mappings (including constitutive relationships and physics/chemistry models). This results in ML models that have a physical meaning and satisfy physics laws and constraints. The prototype of the developed software, called GeoTGO, is accessible through the cloud. Our software prototype demonstrates how different data sources can be made available for processing, executed demonstrative SIML analyses, and presents the results in a table and graphic form.

Keywords: science-informed machine learning, artificial inteligence, exploration, utilization, hidden geothermal

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Authors: Reda Abdel-Aziz

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Agricultural activities in Egypt generate annually around 35 million tons of waste. Composting is one of the most promising technologies to turnover waste in a more economical way, for many centuries. Composting has been used as a mean of recycling organic matter back into the soil to improve soil structure and fertility. Field experiments were conducted in two governorates, Giza and Al-Monofia, to find out the effect of compost with different rates of chemical fertilizers on growth and yield of corn (Zea mays L.) during two constitutive seasons of 2012 and 2013. The experiment, laid out in a randomized complete block design (RCBD), was carried out on five farmers’ fields in each governorate. The treatments were: unfertilized control, full dose of NPK (120, 30, and 50 kg/acre, respectively), compost at rate of 20 ton/acre, compost at rate of 10 ton/acre + 25% of chemical fertilizer, compost at rate of 10 ton/acre + 50% of chemical fertilizer and compost at rate of 10 ton/acre + 75% of chemical fertilizer. Results revealed a superiority of the treatment of compost at rate of 10 ton/acre + 50% of NPK that caused significant improvement in growth, yield and nutrient uptakes of corn in the two governorates during the two constitutive seasons. Results showed that agricultural waste could be composted into value added soil amendment to enhance efficiency of chemical fertilizer. Composting of agricultural waste could also reduce the chemical fertilizers potential hazard to the environment.

Keywords: agricultural waste, compost, chemical fertilizers, corn production, environment

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Authors: Faith-Michael E. Uzoka, Boluwaji A. Akinnuwesi, Taiwo Amoo, Flora Aladi, Stephen Fashoto, Moses Olaniyan, Joseph Osuji

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The overarching aim of this study is to develop a soft-computing system for the differential diagnosis of tropical diseases. These conditions are of concern to health bodies, physicians, and the community at large because of their mortality rates, and difficulties in early diagnosis due to the fact that they present with symptoms that overlap, and thus become ‘confusable’. We report on the first phase of our study, which focuses on the development of a fuzzy cognitive map model for early differential diagnosis of tropical diseases. We used malaria as a case disease to show the effectiveness of the FCM technology as an aid to the medical practitioner in the diagnosis of tropical diseases. Our model takes cognizance of manifested symptoms and other non-clinical factors that could contribute to symptoms manifestations. Our model showed 85% accuracy in diagnosis, as against the physicians’ initial hypothesis, which stood at 55% accuracy. It is expected that the next stage of our study will provide a multi-disease, multi-symptom model that also improves efficiency by utilizing a decision support filter that works on an algorithm, which mimics the physician’s diagnosis process.

Keywords: medical diagnosis, tropical diseases, fuzzy cognitive map, decision support filters, malaria differential diagnosis

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Authors: Abdelghafour Galadi

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In this paper, accurate power MOSFET models including quasi-saturation effect are presented. These models have no internal node voltages determined by the circuit simulator and use one JFET or one depletion mode MOSFET transistors controlled by an “effective” gate voltage taking into account the quasi-saturation effect. The proposed models achieve accurate simulation results with an average error percentage less than 9%, which is an improvement of 21 percentage points compared to the commonly used standard power MOSFET model. In addition, the models can be integrated in any available commercial circuit simulators by using their analytical equations. A description of the models will be provided along with the parameter extraction procedure.

Keywords: power MOSFET, drift layer, quasi-saturation effect, SPICE model

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Authors: Ayman Aboelkassem, Mohamoud Ali, Rezq Diab

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This project aims to document and preserve boat models which were discovered in the Saqqara by Czech Institute of Egyptology archeological mission at Saqqara (GEM numbers, 46007, 46008, 46009). These boat models dates back to Egyptian Old Kingdom and have been transferred to the Conservation Center of the Grand Egyptian Museum, to be displayed at the new museum.The project objectives making such boat models more visible to visitors through the use of 3D reconstructed models and high resolution photos which describe the history of using the boats during the Ancient Egyptian history. Especially, The Grand Egyptian Museum is going to exhibit the second boat of King Khufu from Old kingdom. The project goals are to document the boat models and arrange an exhibition, where such Models going to be displayed next to the Khufu Second Boat. The project shows the importance of using boats in Ancient Egypt, and connecting their usage through Ancient Egyptian periods till now. The boat models had a unique Symbolized in ancient Egypt and connect the public with their kings. The Egyptian kings allowed high ranked employees to put boat models in their tombs which has a great meaning that they hope to fellow their kings in the journey of the afterlife.

Keywords: archaeology, boat models, 3D digital tools for heritage management, museums

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Authors: Edvard P. G. Bruun

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One of the best ways of improving our understanding of reinforced concrete is through large-scale experimental testing. The gathered information is critical in making inferences about structural mechanics and deriving the mathematical models that are the basis for finite element analysis programs and design codes. An effective way of measuring the strains across a region of a specimen is by using a system of surface mounted Linear Variable Differential Transformers (LVDTs). While a single LVDT can only measure the linear strain in one direction, by combining several measurements at known angles a Mohr’s circle of strain can be derived for the whole region under investigation. This paper presents a method that can be used by researchers, which improves the accuracy and removes experimental bias in the calculation of the Mohr’s circle, using four rather than three independent strain measurements. Obtaining high quality strain data is essential, since knowing the angular deviation (shear strain) and the angle of principal strain in the region are important properties in characterizing the governing structural mechanics. For example, the Modified Compression Field Theory (MCFT) developed at the University of Toronto, is a rotating crack model that requires knowing the direction of the principal stress and strain, and then calculates the average secant stiffness in this direction. But since LVDTs can only measure average strains across a plane (i.e., between discrete points), localized cracking and spalling that typically occur in reinforced concrete, can lead to unrealistic results. To build in redundancy and improve the quality of the data gathered, the typical experimental setup for a large-scale shell specimen has four independent directions (X, Y, H, and V) that are instrumented. The question now becomes, which three should be used? The most common approach is to simply discard one of the measurements. The problem is that this can produce drastically different answers, depending on the three strain values that are chosen. To overcome this experimental bias, and to avoid simply discarding valuable data, a more rigorous approach would be to somehow make use of all four measurements. This paper presents the derivation of a method to draw what is effectively a Mohr’s circle of 'best-fit', which optimizes the circle by using all four independent strain values. The four-strain optimized Mohr’s circle approach has been utilized to process data from recent large-scale shell tests at the University of Toronto (Ruggiero, Proestos, and Bruun), where analysis of the test data has shown that the traditional three-strain method can lead to widely different results. This paper presents the derivation of the method and shows its application in the context of two reinforced concrete shells tested in pure torsion. In general, the constitutive models and relationships that characterize reinforced concrete are only as good as the experimental data that is gathered – ensuring that a rigorous and unbiased approach exists for calculating the Mohr’s circle of strain during an experiment, is of utmost importance to the structural research community.

Keywords: reinforced concrete, shell tests, Mohr’s circle, experimental research

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Authors: Suparman

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Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation of piecewise linear regression models. The method used to estimate the parameters of picewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters of picewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.

Keywords: regression, piecewise, Bayesian, reversible Jump MCMC

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Authors: Gyula I. Tóth, Shaho Abdalla

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Even though numerical simulations indeed have a significant precursory/supportive role in exploring the disordered phase displaying no long-range order in pattern formation models, studying the stability properties of this phase and determining the order of the ordered-disordered phase transition in these models necessitate an analytical description of the disordered phase. First, we will present the results of a comprehensive statistical analysis of a large number (1,000-10,000) of numerical simulations in the Swift-Hohenberg model, where the bulk disordered (or amorphous) phase is stable. We will show that the average free energy density (over configurations) converges, while the variance of the energy density vanishes with increasing system size in numerical simulations, which suggest that the disordered phase is a thermodynamic phase (i.e., its properties are independent of the configuration in the macroscopic limit). Furthermore, the structural analysis of this phase in the Fourier space suggests that the phase can be modeled by a colored isotropic Gaussian noise, where any instant of the noise describes a possible configuration. Based on these results, we developed the general mathematical framework of finding a pool of solutions to partial differential equations in the sense of continuous probability measure, which we will present briefly. Applying the general idea to the Swift-Hohenberg model we show, that the amorphous phase can be found, and its properties can be determined analytically. As the general mathematical framework is not restricted to continuum theories, we hope that the proposed methodology will open a new chapter in studying disordered phases.

Keywords: fundamental theory, mathematical physics, continuum models, analytical description

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Authors: Ofosuhene O. Apenteng, Noor Azina Ismail

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Over the last several years, concern has developed over how to minimize the spread of HIV/AIDS epidemic in many countries. AIDS epidemic has tremendously stimulated the development of mathematical models of infectious diseases. The transmission dynamics of HIV infection that eventually developed AIDS has taken a pivotal role of much on building mathematical models. From the initial HIV and AIDS models introduced in the 80s, various improvements have been taken into account as how to model HIV/AIDS frameworks. In this paper, we present the impact of migration on the spread of HIV/AIDS. Epidemic model is considered by a system of nonlinear differential equations to supplement the statistical method approach. The model is calibrated using HIV incidence data from Malaysia between 1986 and 2011. Bayesian inference based on Markov Chain Monte Carlo is used to validate the model by fitting it to the data and to estimate the unknown parameters for the model. The results suggest that the migrants stay for a long time contributes to the spread of HIV. The model also indicates that susceptible individual becomes infected and moved to HIV compartment at a rate that is more significant than the removal rate from HIV compartment to AIDS compartment. The disease-free steady state is unstable since the basic reproduction number is 1.627309. This is a big concern and not a good indicator from the public heath point of view since the aim is to stabilize the epidemic at the disease equilibrium.

Keywords: epidemic model, HIV, MCMC, parameter estimation

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Authors: Mehdi Rostamzadeh

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Genetic Algorithms (GAs) are an adaptive heuristic search algorithm premised on the evolutionary ideas of natural selection and genetic. In this study, we apply GAs for fundamental and technical models of exchange rate determination in exchange rate market. In this framework, we estimated absolute and relative purchasing power parity, Mundell-Fleming, sticky and flexible prices (monetary models), equilibrium exchange rate and portfolio balance model as fundamental models and Auto Regressive (AR), Moving Average (MA), Auto-Regressive with Moving Average (ARMA) and Mean Reversion (MR) as technical models for Iranian Rial against European Union’s Euro using monthly data from January 1992 to December 2014. Then, we put these models into the genetic algorithm system for measuring their optimal weight for each model. These optimal weights have been measured according to four criteria i.e. R-Squared (R2), mean square error (MSE), mean absolute percentage error (MAPE) and root mean square error (RMSE).Based on obtained Results, it seems that for explaining of Iranian Rial against EU Euro exchange rate behavior, fundamental models are better than technical models.

Keywords: exchange rate, genetic algorithm, fundamental models, technical models

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Authors: Fatih Tarlak

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Predictive microbiology can be considered as an important field in food microbiology in which it uses predictive models to describe the microbial growth in different food products. Predictive models estimate the growth of microorganisms quickly, efficiently, and in a cost-effective way as compared to traditional methods of enumeration, which are long-lasting, expensive, and time-consuming. The mathematical models used in predictive microbiology are mainly categorised as primary and secondary models. The primary models are the mathematical equations that define the growth data as a function of time under a constant environmental condition. The secondary models describe the effects of environmental factors, such as temperature, pH, and water activity (aw) on the parameters of the primary models, including the maximum specific growth rate and lag phase duration, which are the most critical growth kinetic parameters. The combination of primary and secondary models provides valuable information to set limits for the quantitative detection of the microbial spoilage and assess product shelf-life.

Keywords: shelf-life, growth model, predictive microbiology, simulation

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Authors: Wenya Shu, Ilinca Stanciulescu

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Carbon nanotubes (CNTs) possess attractive properties, such as high stiffness and strength, and high thermal and electrical conductivities, making them promising filler in multifunctional nanocomposites. Although CNTs can be efficient reinforcements, the expected level of mechanical performance of CNT-polymers is not often reached in practice due to the poor mechanical behavior of the CNT-polymer interfaces. It is believed that the interactions of CNT and polymer mainly result from the Van der Waals force. The interface debonding is a fracture and delamination phenomenon. Thus, the cohesive zone modeling (CZM) is deemed to give good capture of the interface behavior. The detailed, cohesive zone modeling provides an option to consider the CNT-matrix interactions, but brings difficulties in mesh generation and also leads to high computational costs. Homogenized models that smear the fibers in the ground matrix and treat the material as homogeneous are studied in many researches to simplify simulations. But based on the perfect interface assumption, the traditional homogenized model obtained by mixing rules severely overestimates the stiffness of the composite, even comparing with the result of the CZM with artificially very strong interface. A mechanical model that can take into account the interface debonding and achieve comparable accuracy to the CZM is thus essential. The present study first investigates the CNT-matrix interactions by employing cohesive zone modeling. Three different coupled CZM laws, i.e., bilinear, exponential and polynomial, are considered. These studies indicate that the shapes of the CZM constitutive laws chosen do not influence significantly the simulations of interface debonding. Assuming a bilinear traction-separation relationship, the debonding process of single CNT in the matrix is divided into three phases and described by differential equations. The analytical solutions corresponding to these phases are derived. A homogenized model is then developed by introducing a parameter characterizing interface sliding into the mixing theory. The proposed mechanical model is implemented in FEAP8.5 as a user material. The accuracy and limitations of the model are discussed through several numerical examples. The CZM simulations in this study reveal important factors in the modeling of CNT-matrix interactions. The analytical solutions and proposed homogenized model provide alternative methods to efficiently investigate the mechanical behaviors of CNT/polymer composites.

Keywords: carbon nanotube, cohesive zone modeling, homogenized model, interface debonding

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Authors: Malika El Kyal, Ahmed Machmoum

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We prove the superlinear convergence of asynchronous multi-splitting methods applied to differential equations. This study is based on the technique of nested sets. It permits to specify kind of the convergence in the asynchronous mode.The main characteristic of an asynchronous mode is that the local algorithm not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays to be substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: parallel methods, asynchronous mode, multisplitting, ODE

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Authors: Md Al Masum Bhuiyan, Maria C. Mariani, Osei K. Tweneboah

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In the present work, we develop a technique for estimating the volatility of financial time series by using stochastic differential equation. Taking the daily closing prices from developed and emergent stock markets as the basis, we argue that the incorporation of stochastic volatility into the time-varying parameter estimation significantly improves the forecasting performance via Maximum Likelihood Estimation. While using the technique, we see the long-memory behavior of data sets and one-step-ahead-predicted log-volatility with ±2 standard errors despite the variation of the observed noise from a Normal mixture distribution, because the financial data studied is not fully Gaussian. Also, the Ornstein-Uhlenbeck process followed in this work simulates well the financial time series, which aligns our estimation algorithm with large data sets due to the fact that this algorithm has good convergence properties.

Keywords: financial time series, maximum likelihood estimation, Ornstein-Uhlenbeck type models, stochastic volatility model

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Authors: Somar Boubou, Tatsuo Narikiyo, Michihiro Kawanishi

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In this work, we address the problem of 3D object recognition with depth sensors such as Kinect or Structure sensor. Compared with traditional approaches based on local descriptors, which depends on local information around the object key points, we propose a global features based descriptor. Proposed descriptor, which we name as Differential Histogram of Normal Vectors (DHONV), is designed particularly to capture the surface geometric characteristics of the 3D objects represented by depth images. We describe the 3D surface of an object in each frame using a 2D spatial histogram capturing the normalized distribution of differential angles of the surface normal vectors. The object recognition experiments on the benchmark RGB-D object dataset and a self-collected dataset show that our proposed descriptor outperforms two others descriptors based on spin-images and histogram of normal vectors with linear-SVM classifier.

Keywords: vision in control, robotics, histogram, differential histogram of normal vectors

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Authors: Helmi Temimi

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In this paper, we study the super-convergence properties of the discontinuous Galerkin (DG) method applied to one-dimensional mth-order ordinary differential equations without introducing auxiliary variables. We found that nth−derivative of the DG solution exhibits an optimal O (hp+1−n) convergence rates in the L2-norm when p-degree piecewise polynomials with p≥1 are used. We further found that the odd-derivatives and the even derivatives are super convergent, respectively, at the upwind and downwind endpoints.

Keywords: discontinuous, galerkin, superconvergence, higherorder, error, estimates

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Authors: Gleda Kutrolli, Maksi Kutrolli, Etjon Meco

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SARS-CoV-2 virus is currently one of the most infectious pathogens for humans. It started in China at the end of 2019 and now it is spread in all over the world. The origin and diffusion of the SARS-CoV-2 epidemic, is analysed based on the discussion of viral phylogeny theory. With the aim of understanding the spread of infection in the affected countries, it is crucial to modelize the spread of the virus and simulate its activity. In this paper, the prediction of coronavirus outbreak is done by using SIR model without vital dynamics, applying different numerical technique solving ordinary differential equations (ODEs). We find out that ABM and MRT methods perform better than other techniques and that the activity of the virus will decrease in April but it never cease (for some time the activity will remain low) and the next cycle will start in the middle July 2020 for Norway and Denmark, and October 2020 for Sweden, and September for Finland.

Keywords: forecasting, ordinary differential equations, SARS-COV-2 epidemic, SIR model

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Authors: Alfred L. Guiffrida

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A review of the literature on supply chain delivery models which use delivery windows to measure delivery performance is presented. The review herein serves to meet the following objectives: (i) provide a synthesis of previously published literature on supply chain delivery performance models, (ii) provide in one paper a consolidation of research that can serve as a single source to keep researchers up to date with the research developments in supply chain delivery models, and (iii) identify gaps in the modeling of supply chain delivery performance which could stimulate new research agendas.

Keywords: delivery performance, delivery window, supply chain delivery models, supply chain performance

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Authors: Jamshid Qodirov, Sirojiddin Komolov, Ravilov Mirahmad, Olimjon Mirzayev

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Nowadays, natural language processing tools play a crucial role in our daily lives, including various techniques with text processing. There are very advanced models in modern languages, such as English, Russian etc. But, in some languages, such as Uzbek, the NLP models have been developed recently. Thus, there are only a few NLP models in Uzbek language. Moreover, there is no such work that could show which Uzbek NLP model behaves in different situations and when to use them. This work tries to close this gap and compares the Uzbek NLP models existing as of the time this article was written. The authors try to compare the NLP models in two different scenarios: sentiment analysis and sentence similarity, which are the implementations of the two most common problems in the industry: classification and similarity. Another outcome from this work is two datasets for classification and sentence similarity in Uzbek language that we generated ourselves and can be useful in both industry and academia as well.

Keywords: NLP, benchmak, bert, vectorization

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Authors: Chinmayee Choudhury

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Human Melanocortin 4 Receptor (HMC4R) is one of the most potential drug targets for the treatment of obesity which controls the appetite. A deletion of the residues 88-92 in HMC4R is sometimes the cause of severe obesity in the humans. In this study, two homology models are constructed for the normal as well as mutated HMC4Rs and some phytochemicals present in Green Tea, Honey and Cinnamon have been docked to them to study their differential binding to the normal and mutated HMC4R as compared to the natural agonist α- MSH. Two homology models have been constructed for the normal as well as mutated HMC4Rs using the Modeller9v7. Some of the phytochemicals present in Green Tea, Honey, and Cinnamon, which have appetite suppressant activities are constructed, minimized and docked to these normal and mutated HMC4R models using ArgusLab 4.0.1. The mode of binding of the phytochemicals with the Normal and Mutated HMC4Rs have been compared. Further, the mode of binding of these phytochemicals with that of the natural agonist α- Melanocyte Stimulating Hormone(α-MSH) to both normal and mutated HMC4Rs have also been studied. It is observed that the phytochemicals Kaempherol, Epigallocatechin-3-gallate (EGCG) present in Green Tea and Honey, Isorhamnetin, Chlorogenic acid, Chrysin, Galangin, Pinocambrin present in Honey, Cinnamaldehyde, Cinnamyl acetate and Cinnamyl alcohol present in Cinnamon have capacity to form more stable complexes with the Mutated HMC4R as compared to α- MSH. So they may be potential agonists of HMC4R to suppress the appetite.

Keywords: HMC4R, α-MSH, docking, photochemical, appetite suppressant, homology modelling

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Authors: Lina Wu, Ye Li, Jia Liu

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We are interested in solving Liouville-type problems to explore constancy properties for maps or differential forms on Riemannian manifolds. Geometric structures on manifolds, the existence of constancy properties for maps or differential forms, and energy growth for maps or differential forms are intertwined. In this article, we concentrate on discovery of solutions to Liouville-type problems where manifolds are Euclidean spaces (i.e. flat Riemannian manifolds) and maps become real-valued functions. Liouville-type results of vanishing properties for functions are obtained. The original work in our research findings is to extend the q-energy for a function from finite in L^q space to infinite in non-L^q space by applying p-balanced technique where q = p = 2. Calculation skills such as Hölder's Inequality and Tests for Series have been used to evaluate limits and integrations for function energy. Calculation ideas and computational techniques for solving Liouville-type problems shown in this article, which are utilized in Euclidean spaces, can be universalized as a successful algorithm, which works for both maps and differential forms on Riemannian manifolds. This innovative algorithm has a far-reaching impact on research work of solving Liouville-type problems in the general settings involved with infinite energy. The p-balanced technique in this algorithm provides a clue to success on the road of q-energy extension from finite to infinite.

Keywords: differential forms, holder inequality, Liouville-type problems, p-balanced growth, p-harmonic maps, q-energy growth, tests for series

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Authors: Gilbert Makanda

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The problem of the teaching of mathematics is studied using differential equations. A mathematical model for knowledge acquisition in mathematics is developed. In this study we adopt the mathematical model that is normally used for disease modelling in the teaching of mathematics. It is assumed that teaching is 'infecting' students with knowledge thereby spreading this knowledge to the students. It is also assumed that students who gain this knowledge spread it to other students making disease model appropriate to adopt for this problem. The results of this study show that increasing recruitment rates, learning contact with teachers and learning materials improves the number of knowledgeable students. High dropout rates and forgetting taught concepts also negatively affect the number of knowledgeable students. The developed model is then solved using Matlab ODE45 and \verb"lsqnonlin" to estimate parameters for the actual data.

Keywords: differential equations, knowledge acquisition, least squares, dynamical systems

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Authors: Marian Sorin Ionescu, Olivia Negoita, Cosmin Dobrin

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This scientific communication reports and discusses learning models adaptable to modern business problems and models specific to digital concepts and paradigms. In the PAC (probably approximately correct) learning model approach, in which the learning process begins by receiving a batch of learning examples, the set of learning processes is used to acquire a hypothesis, and when the learning process is fully used, this hypothesis is used in the prediction of new operational examples. For complex business models, a lot of models should be introduced and evaluated to estimate the induced results so that the totality of the results are used to develop a predictive rule, which anticipates the choice of new models. In opposition, for online learning-type processes, there is no separation between the learning (training) and predictive phase. Every time a business model is approached, a test example is considered from the beginning until the prediction of the appearance of a model considered correct from the point of view of the business decision. After choosing choice a part of the business model, the label with the logical value "true" is known. Some of the business models are used as examples of learning (training), which helps to improve the prediction mechanisms for future business models.

Keywords: machine learning, business models, convex analysis, online learning

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Authors: F. Waffo Tchuimmo, G. S. Kwandio Dongoua, C. U. Yves Mbono Samba, O. Dafounansou, L. Nana

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The strength criterion is an important condition of great interest to guarantee the stability of the structural elements. The present work is based on the study of the free vibration of Euler’s Bernoulli column of equal strength in compression while considering its own weight and the axial load in compression and tension subjected to symmetrical boundary conditions. We use the differential quadrature method to investigate the first fifth naturals frequencies parameters of the column according to the different forms of geometrical sections. The results of this work give help in making a judicious choice of type of cross-section and a better boundary condition to guarantee good stability of this type of column in civil constructions.

Keywords: free vibration, equal strength, self-weight, tip force, differential quadrature method

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Authors: H. Dakhlaoui, D. Ruelland, Y. Tramblay, Z. Bargaoui

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To evaluate the impact of climate change on water resources at the catchment scale, not only future projections of climate are necessary but also robust rainfall-runoff models that are able to be fairly reliable under changing climate conditions. This study aims at assessing the robustness of three conceptual rainfall-runoff models (GR4j, HBV and IHACRES) on five basins in Northern Tunisia under long-term climate variability. Their robustness was evaluated according to a differential split sample test based on a climate classification of the observation period regarding simultaneously precipitation and temperature conditions. The studied catchments are situated in a region where climate change is likely to have significant impacts on runoff and they already suffer from scarcity of water resources. They cover the main hydrographical basins of Northern Tunisia (High Medjerda, Zouaraâ, Ichkeul and Cap bon), which produce the majority of surface water resources in Tunisia. The streamflow regime of the basins can be considered as natural since these basins are located upstream from storage-dams and in areas where withdrawals are negligible. A 30-year common period (1970‒2000) was considered to capture a large spread of hydro-climatic conditions. The calibration was based on the Kling-Gupta Efficiency (KGE) criterion, while the evaluation of model transferability is performed according to the Nash-Suttfliff efficiency criterion and volume error. The three hydrological models were shown to have similar behaviour under climate variability. Models prove a better ability to simulate the runoff pattern when transferred toward wetter periods compared to the case when transferred to drier periods. The limits of transferability are beyond -20% of precipitation and +1.5 °C of temperature in comparison with the calibration period. The deterioration of model robustness could in part be explained by the climate dependency of some parameters.

Keywords: rainfall-runoff modelling, hydro-climate variability, model robustness, uncertainty, Tunisia

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Authors: S. S. Abas, Y. M. Yatim

Abstract:

In this paper the unsteady, slender, symmetric dry patch in an infinitely wide and thin liquid film of Newtonian fluid draining under gravity down an inclined plane in the presence of strong surface-tension effect is considered. A similarity transformation, named a travelling-wave similarity solution is used to reduce the governing partial differential equation into the ordinary differential equation which is then solved numerically using a shooting method. The introduction of surface-tension effect on the flow leads to a fourth-order ordinary differential equation. The solution obtained predicts that the dry patch has a quartic shape and the free surface has a capillary ridge near the contact line which decays in an oscillatory manner far from it.

Keywords: dry patch, Newtonian fluid, similarity solution, surface-tension effect, travelling-wave, unsteady thin-film flow

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Authors: Surendra Kumar Patel

Abstract:

Disability is not just a health problem; it is a complex phenomenon, reflecting the interaction between features of a person’s age and physiology. Population ageing is a major demographic issue for India in the 21st century. Older population of India constituted 8% of total population, while 5.19% has affected by disability of older age group. Objective of the present research paper is to examine the state wise differential in disability among 60+ population and to access the health care of disabled population especially the 60+ disabled persons. The data sources of the present paper are census 2001 and 2011. For analyzing the state wise differentials by disability types and comparative advantage of data, rate, ratio, and percentage have been used. The Standardized Index of Diversity of Disability (SIDD) studies differential and diversity in disability. The results show that there are 5.19% persons have disability among 60+ population and sex differential not very significant, as it is 5.3 % of male and 5.05% in female in India but place of residence shows significant variation from 2001 to 2011 census. There is huge diversity in disability prevalence among 60+ in India, highest in Sikkim followed by Rajasthan, approximately, they comprise 11%, and the lowest found in Tamil Nadu as 2.53%. This huge gap in prevalence percentage shows the health care needs of highly prevailing states.

Keywords: disability, Standardized Index of Diversity of Disability (SIDD), differential and diversity in disability, 60+ population

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