Search results for: Linear/nonlinear plants

Authors: Sophia Fry, Mahir Irtiza, Alexa Hoffman, Yousef Sardahi

Abstract:

This study presents an intelligent control algorithm for a flexible robotic arm. Fuzzy control is used to control the motion of the arm to maintain the arm tip at the desired position while reducing vibration and increasing the system speed of response. The Fuzzy controller (FC) is based on adding the tip angular position to the arm deflection angle and using their sum as a feedback signal to the control algorithm. This reduces the complexity of the FC in terms of the input variables, number of membership functions, fuzzy rules, and control structure. Also, the design of the fuzzy controller is model-free and uses only our knowledge about the system. To show the efficacy of the FC, the control algorithm is implemented on the flexible joint manipulator (FJM) developed by Quanser. The results show that the proposed control method is effective in terms of response time, overshoot, and vibration amplitude.

Keywords: Fuzzy logic control, model-free control, flexible joint manipulators, nonlinear control.

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Authors: Hamed Zakikhani, Mohd Khanif Yusop, Amin Soltangheisi

Abstract:

A hydroponic trial was carried out to investigate the effect of molybdenum (Mo) on uptake of phosphorus (P) in different rice cultivars. The experiment was conducted using a randomized complete-block design, with a split-plot arrangement of treatments and three replications. Four rates of Mo (0, 0.01, 0.1 and 1 mg L⁻¹) and five cultivars (MR219, HASHEMI, MR232, FAJRE and MR253) provided the main and sub-plots, respectively. Interaction of molybdenum×variety was significant on shoot phosphorus uptake (p≤0.01). Highest and lowest shoot phosphorus uptake were seen in Mo₃V₃ (0.6% plant^-1) and Mo₀V₃ (0.14% plant^-1) treatments, respectively. Molybdenum did not have a significant effect on root phosphorus content. According to results, application of molybdenum has a synergistic effect on uptake of phosphorus by rice plants.

Keywords: Molybdenum, Phosphorus, Uptake, rice.

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Authors: Fan-Yong Meng

Abstract:

In this paper, a generalized form of the Banzhaf-Owen value for cooperative fuzzy games with a coalition structure is proposed. Its axiomatic system is given by extending crisp case. In order to better understand the Banzhaf-Owen value for fuzzy games with a coalition structure, we briefly introduce the Banzhaf-Owen values for two special kinds of fuzzy games with a coalition structure, and give their explicit forms.

Keywords: Cooperative fuzzy game, Banzhaf-Owen value, multi linear extension, Choquet integral.

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Authors: Xuan Sun, Mingbo Tong

Abstract:

To understand the factors which affect impact damage on composite structures, particularly the effects of impact position and ribs. In this paper, a finite element model (FEM) of low-velocity impact damage on the composite structure was established via the nonlinear finite element method, combined with the user-defined materials subroutine (VUMAT) of the ABAQUS software. The structural elements chosen for the investigation comprised a series of stiffened composite panels, representative of real aircraft structure. By impacting the panels at different positions relative to the ribs, the effect of relative position of ribs was found out. Then the simulation results and the experiments data were compared. Finally, the factors which affect impact damage on the structures were discussed. The paper was helpful for the design of stiffened composite structures.

Keywords: Stiffened, Low-velocity, Impact, Abaqus, Impact Energy.

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Authors: Taïeb Branci, Djamal Yahmi, Abdelhamid Bouchair, Eric Fourneley

Abstract:

According to current seismic codes the structures are calculated using the capacity design procedure based on the concept of shear at the base depending on several parameters including behavior factor which is considered to be the most important parameter. The behavior factor allows designing the structure when it is at its ultimate limit state taking into account its energy dissipation through its plastic deformation. The aim of the present study is to assess the basic parameters on which is composed the behavior factor among them the reduction factor due to ductility, and those due to redundancy and the overstrength for steel moment-resisting frames of different heights and regular configuration. Analyses are conducted on these frames using the nonlinear static method where the effect of some parameters on the behavior factor, such as the number of stories and the number of spans, are taken into account. The results show that the behavior factor is rather sensitive to the variation of the number of stories and bays.

Keywords: Behavior, code, frame, ductility, overstrength, redundancy, plastic.

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Authors: Rida B. Arieby, Hameed N. Hameed

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In this work, tensile tests on high density polyethylene have been carried out under various constant strain rate and strain rate jump tests. The dependency of the true stress and specially the variation of volume strain have been investigated, the volume strain due to the phenomena of damage was determined in real time during the tests by an optical extensometer called Videotraction. A modified constitutive equations, including strain rate and damage effects, are proposed, such a model is based on a non-equilibrium thermodynamic approach called (DNLR). The ability of the model to predict the complex nonlinear response of this polymer is examined by comparing the model simulation with the available experimental data, which demonstrate that this model can represent the deformation behavior of the polymer reasonably well.

Keywords: Strain rate jump tests, Volume Strain, High Density Polyethylene, Large strain, Thermodynamics approach.

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Authors: Shuo-Li Hsu, Peng-Wei Gau, I-Lin Wu, Jyh-Horng Jeng

Abstract:

For most image fusion algorithms separate relationship by pixels in the image and treat them more or less independently. In addition, they have to be adjusted different parameters in different time or weather. In this paper, we propose a region–based image fusion which combines aspects of feature and pixel-level fusion method to replace only by pixel. The basic idea is to segment far infrared image only and to add information of each region from segmented image to visual image respectively. Then we determine different fused parameters according different region. At last, we adopt artificial neural network to deal with the problems of different time or weather, because the relationship between fused parameters and image features are nonlinear. It render the fused parameters can be produce automatically according different states. The experimental results present the method we proposed indeed have good adaptive capacity with automatic determined fused parameters. And the architecture can be used for lots of applications.

Keywords: Image fusion, Region-based fusion, Segmentation, Neural network, Multi-sensor.

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Authors: Mada Sanjaya, Halimatussadiyah, Dian Syah Maulana

Abstract:

The nonlinear chaotic non-autonomous fourth order system is algebraically simple but can generate complex chaotic attractors. In this paper, non-autonomous fourth order chaotic oscillator circuits were designed and simulated. Also chaotic nonautonomous Attractor is addressed suitable for chaotic masking communication circuits using Matlab® and MultiSIM® programs. We have demonstrated in simulations that chaos can be synchronized and applied to signal masking communications. We suggest that this phenomenon of chaos synchronism may serve as the basis for little known chaotic non-autonomous Attractor to achieve signal masking communication applications. Simulation results are used to visualize and illustrate the effectiveness of non-autonomous chaotic system in signal masking. All simulations results performed on nonautonomous chaotic system are verify the applicable of secure communication.

Keywords: Bidirectional chaotic synchronization, double bellattractor, secure communication

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Authors: Kejun Zhuang, Hailong Zhu

Abstract:

In this paper, stability and Hopf bifurcation analysis of a novel hyperchaotic system are investigated. Four feedback control strategies, the linear feedback control method, enhancing feedback control method, speed feedback control method and delayed feedback control method, are used to control the hyperchaotic attractor to unstable equilibrium. Moreover numerical simulations are given to verify the theoretical results.

Keywords: Feedback control, Hopf bifurcation, hyperchaotic system, stability.

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Authors: Nilima D. Gajbhiye

Abstract:

Sodium nitrate has been used industrially in a number of work fields ranging from agriculture to food industry. Sodium nitrate and nitrite are associated with a higher risk of cancer in human beings. In present study, the effect of sodium nitrate on germinating seeds was studied. Two different sets of ungerminated Vigna radiata seeds were taken. In one set Vigna radiata seeds were soaked in distilled water for 4 hours and they were allowed to germinate in distilled water (Control) and 0.1 to 1% and 10% concentrations of sodium nitrate (NaNo₃). In soaked seed set, on 2^nd day radical developed in control and 0.1 to 1% concentrations of sodium nitrate. Seeds size was enlarged in 1% and 10% concentrations of sodium nitrate. On 3^rd day in 0.1% sodium nitrate length of the radicle was 7.5cm with one leaf let and control sample showed 9cm with one leaflet. On 5^th day in 0.1% sodium nitrate length of the radicle was 10 cm with one leaf let and control sample showed 11.5cm with one leaflet. No radicle developed in 1 and 10% NaNo₃ concentrations. On 10^th day all plants including control were dead. More number of mitotic cells was observed in apical root meristems of control germinating seeds and less mitotic cells were observed in 0.1% NaNo₃ germinating seeds. But cells were elongated in 0.9%NaNo₃ concentration and particles are deposited in the cells and no mitotic cells were observed. In other sets, dry seeds were allowed to germinate in Distilled water (control) and in 0.1 to 1% and 10% concentrations of sodium nitrate. In dry seed set, on 2^nd day radicle developed from control set. In 0.1 to 1% concentrations of sodium nitration seed enlarged in size but but not allowed germination. But in 10% NaNo₃ seeds coat colour was changed from dark green to brown. On 3^rd day the radicle was developed in 0.1% concentration of NaNo₃. No growth of radicle was observed in 0.3 to 10% concentrations of NaNo₃ but plumule was observed in control plant. Seed coat color was changed from dark green to brown in color in 1% and 10% NaNo₃. On 5^th day in control seeds the radicle growth was 11cm and 0.1% NaNo₃ concentration was 1.3 cm. On 10^th day all plants including control were dead. More number of mitotic cells was observed in apical root meristems of control germinating seeds and less mitotic cells were observed in 0.1% NaNo3 germinating seeds. At higher concentrations of NaNo₃ allowed seed germination in soaked seeds but produced radicle decay. In comparison to it, in dry seed set, germination of seeds observed only in 0.1% NaNo₃ concentration. The inhibitory effect of NaNo₃ on seed germination is due to reduction of water imbibition and mitotic activity.

Keywords: Germinating seeds, NaNo3, Vigna radiate, mitotic activity.

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Authors: Düzgün Akmaz, Hüseyin Erişti

Abstract:

In the last few years, harmonics have been occurred with the increasing use of nonlinear loads, and these harmonics have been an ever increasing problem for the line systems. This situation importantly affects the quality of power and gives large losses to the network. An efficient way to solve these problems is providing harmonic compensation through parallel active power filters. Many methods can be used in the control systems of the parallel active power filters which provide the compensation. These methods efficiently affect the performance of the active power filters. For this reason, the chosen control method is significant. In this study, Fourier analysis (FA) control method and synchronous reference frame (SRF) control method are discussed. These control methods are designed for both eliminate harmonics and perform reactive power compensation in MATLAB/Simulink pack program and are tested. The results have been compared for each two methods.

Keywords: Harmonics, Harmonic compensation, Parallel active power filters, Power quality.

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Authors: Guangyu Liu

Abstract:

In the last decade, energy based control theory has undergone a significant breakthrough in dealing with underactated mechanical systems with two successful and similar tools, controlled Lagrangians and controlled Hamiltanians (IDA-PBC). However, because of the complexity of these tools, successful case studies are lacking, in particular, MIMO cases. The seminal theoretical paper of controlled Lagrangians proposed by Bloch and his colleagues presented a benchmark example–a 4 d.o.f underactuated pendulum on a cart but a detailed and completed design is neglected. To compensate this ignorance, the note revisit their design idea by addressing explicit control functions for a similar device motivated by a vector thrust body hovering in the air. To the best of our knowledge, this system is the first MIMO, underactuated example that is stabilized by using energy based tools at the courtesy of the original design idea. Some observations are given based on computer simulation.

Keywords: Controlled Lagrangian, Energy Shaping, Spherical Inverted Pendulum, Controlled Hamiltonian.

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Authors: Seok Hyoung Lee, Vladimir Shin

Abstract:

An optimal mean-square fusion formulas with scalar and matrix weights are presented. The relationship between them is established. The fusion formulas are compared on the continuous-time filtering problem. The basic differential equation for cross-covariance of the local errors being the key quantity for distributed fusion is derived. It is shown that the fusion filters are effective for multi-sensor systems containing different types of sensors. An example demonstrating the reasonable good accuracy of the proposed filters is given.

Keywords: Kalman filtering, fusion formula, multi-sensor, mean-square error.

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Authors: Marine Shavlakadze

Abstract:

Hydroponic greenhouses systems (production of the artificial substrate without soil) are becoming popular in the world. Mostly the system is used to grow vegetables and berries. Different countries are taking action to participate in the development of hydroponic technology and solutions such as EU members, Turkey, Australia, New Zealand, Israel, Scandinavian countries, etc. Many vegetables and berries are grown by hydroponics in Europe. As a result of our research, we have obtained material containing manganese and nitrogen. It became possible to produce this fertilizer by means of one-stage thermal processing, using industrial waste containing manganese (ores and sludges) and mineral substance (ammonium nitrate) that exist in Georgia. The received material is usable as a micro-fertilizer with economic efficiency. It became possible to turn practically water-insoluble manganese dioxide substance into the soluble condition from industrial waste in an indirect way. The ability to use the material as a fertilizer is predetermined by its chemical and phase composition, as the amount of the active component of the material in relation to manganese is 30%. At the same time, the active component elements presented non-ballast sustained action compounds. The studies implemented in Poland and in Georgia by us have shown that the manganese-containing micro-fertilizer- Mn(NO₃)₂ can provide the plant with nitrate nitrogen, which is a form that can be used for plants, providing the economy and simplicity of the application of fertilizers. Given the fact that the application of the manganese-containing micro-fertilizers significantly increases the productivity and improves the quality of the big number of agricultural products, it is necessary to mention that it is recommended to introduce the manganese containing fertilizers into the following cultures: sugar beet, corn, potato, vegetables, vine grape, fruit, berries, and other cultures. Also, as a result of the study, it was established that the material obtained is the predominant fertilizer for vegetable cultures in the soil. Based on the positive results of the research, we consider it expedient to conduct research in hydroponic systems, which will enable us to provide plants the required amount of manganese; we also introduce nitrogen in solution and regulate the solution of pH, which is one of the main problems in hydroponic production. The findings of our research will be used in hydroponic greenhouse farms to increase the fertility of vegetable crops and, consequently, to get bountiful and high-quality harvests, which will promote the development of hydroponic greenhouses in Georgia as well as abroad.

Keywords: Hydroponics, micro-fertilizers, manganese ore, chemical amelioration.

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Authors: Daniel Y. Abebe, Sijeong Jeong, Jaehyouk Choi

Abstract:

The use of eccentrically braced frame (EBF) is increasing day by day as EBF possesses high elastic stiffness, stable inelastic response under cyclic lateral loading, and excellent ductility and energy dissipation capacity. The ductility and energy dissipation capacity of EBF depends on the active link beams. Recently, there are two types EBFs; these are conventional EBFs and EBFs with replaceable links. The conventional EBF has a disadvantage during maintenance in post-earthquake. The concept of removable active link beam in EBF is developed to overcome the limitation of the conventional EBF in post-earthquake. In this study, a replaceable link with reduced web section is introduced and design equations are suggested. In addition, nonlinear finite element analysis was conducted in order to evaluate the proposed links.

Keywords: EBFs, replaceable link, earthquake disaster, reduced section.

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Authors: Fatemeh Panjeh Ali Beik

Abstract:

In the present work, we propose a new method for solving the matrix equation AXB=F . The new method can be considered as a generalized form of the well-known global full orthogonalization method (Gl-FOM) for solving multiple linear systems. Hence, the method will be called extended Gl-FOM (EGl- FOM). For implementing EGl-FOM, generalized forms of block Krylov subspace and global Arnoldi process are presented. Finally, some numerical experiments are given to illustrate the efficiency of our new method.

Keywords: Matrix equations, Iterative methods, Block Krylovsubspace methods.

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Authors: M. H. Moradi, S. M. Moosavi, A. R. Reisi

Abstract:

The main objective of this paper is to investigate the enhancement of power system stability via coordinated tuning of Power System Stabilizers (PSSs) in a multi-machine power system. The design problem of the proposed controllers is formulated as an optimization problem. Chaotic catfish particle swarm optimization (C-Catfish PSO) algorithm is used to minimize the ITAE objective function. The proposed algorithm is evaluated on a two-area, 4- machines system. The robustness of the proposed algorithm is verified on this system under different operating conditions and applying a three-phase fault. The nonlinear time-domain simulation results and some performance indices show the effectiveness of the proposed controller in damping power system oscillations and this novel optimization algorithm is compared with particle swarm optimization (PSO).

Keywords: Power system stabilizer, C-Catfish PSO, ITAE objective function, Power system control, Multi-machine power system

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Authors: M. Nayeripour, T. Niknam

Abstract:

Nonlinear and unbalance loads in three phase networks create harmonics and losses. Active and passive filters are used for elimination or reduction of these effects. Passive filters have some limitations. For example, they are designed only for a specific frequency and they may cause to resonance in the network at the point of common coupling. The other drawback of a passive filter is that the sizes of required elements are normally large. The active filter can improve some of limitations of passive filter for example; they can eliminate more than one harmonic and don't cause resonance in the network. In this paper inverter analysis have been done simultaneously in three phase and the RL impedance of the line have been considered. A sliding mode control based on energy feedback of capacitors is employed in the design with this method, the dynamic speed of the filter is improved effectively and harmonics and load unbalance is compensating quickly.

Keywords: Shunt active filter, harmonic, inverter, sliding mode control, energy feedback.

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Authors: Tahmine. V. Moghaddam, N. Bigdeli, K. Afshar

Abstract:

To achieve the desired specifications of gain and phase margins for plants with time-delay that stabilized with FO-PID controller a lead compensator is designed. At first the range of controlled system stability based on stability boundary criteria is determined. Using stability boundary locus method in frequency domain the fractional order controller parameters are tuned and then with drawing bode diagram in frequency domain accessing to desired gain and phase margin are shown. Numerical examples are given to illustrate the shapes of the stabilizing region and to show the design procedure.

Keywords: Fractional controller, Lead compensator, Stabilityregions, Stability boundary locus

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Authors: Mário C. Ricci

Abstract:

A new, rapidly convergent, numerical procedure for internal loading distribution computation in statically loaded, singlerow, angular-contact ball bearings, subjected to a known combined radial and thrust load, which must be applied so that to avoid tilting between inner and outer rings, is used to find the load distribution differences between a loaded unfitted bearing at room temperature, and the same loaded bearing with interference fits that might experience radial temperature gradients between inner and outer rings. For each step of the procedure it is required the iterative solution of Z + 2 simultaneous nonlinear equations – where Z is the number of the balls – to yield exact solution for axial and radial deflections, and contact angles.

Keywords: Ball, Bearing, Static, Load, Iterative, Numerical, Method, Temperature, Fit.

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Authors: P. Georgieva, S. Feyo de Azevedo

Abstract:

This paper is focused on issues of process modeling and two model based control strategies of a fed-batch sugar crystallization process applying the concept of artificial neural networks (ANNs). The control objective is to force the operation into following optimal supersaturation trajectory. It is achieved by manipulating the feed flow rate of sugar liquor/syrup, considered as the control input. The control task is rather challenging due to the strong nonlinearity of the process dynamics and variations in the crystallization kinetics. Two control alternatives are considered – model predictive control (MPC) and feedback linearizing control (FLC). Adequate ANN process models are first built as part of the controller structures. MPC algorithm outperforms the FLC approach with respect to satisfactory reference tracking and smooth control action. However, the MPC is computationally much more involved since it requires an online numerical optimization, while for the FLC an analytical control solution was determined.

Keywords: artificial neural networks, nonlinear model control, process identification, crystallization process

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Authors: Belkacem Brahmi, Mohand Ouamer Bibi

Abstract:

In this paper, we present a new method for solving quadratic programming problems, not strictly convex. Constraints of the problem are linear equalities and inequalities, with bounded variables. The suggested method combines the active-set strategies and support methods. The algorithm of the method and numerical experiments are presented, while comparing our approach with the active set method on randomly generated problems.

Keywords: Convex quadratic programming, dual support methods, active set methods.

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Authors: Adnene Arbi, Chaouki Aouiti, Abderrahmane Touati

Abstract:

In this paper, we consider the global exponential stability of the equilibrium point of Hopfield neural networks with delays and impulsive perturbation. Some new exponential stability criteria of the system are derived by using the Lyapunov functional method and the linear matrix inequality approach for estimating the upper bound of the derivative of Lyapunov functional. Finally, we illustrate two numerical examples showing the effectiveness of our theoretical results.

Keywords: Hopfield Neural Networks, Exponential stability.

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Authors: Yi-Fang Hung, Jinn-Tsyy Lai

Abstract:

Lycopene, which can be extracted from plants and is very popular for fruit intake, is restricted for healthy food development due to its high price. On the other hand, it will get great safety concerns, especially in the food or cosmetic application, if the raw material of lycopene is produced by chemical synthesis. In this project, we provide a key technology to bridge the limitation as mentioned above. Based on the abundant bioresources of BCRC (Bioresource Collection and Research Center, Taiwan), a promising lycopene output will be anticipated by the introduction of fermentation technology along with industry-related core energy. Our results showed that addition of tween 80(0.2%) and span 20 produced higher amount of lycopene. And piperidine, when was added at 48hr to the cultivation medium, could promote lycopene excretion effectively also.

Keywords: photosynthetic bacteria, lycopene, tween80, Piperidine

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Authors: Swathi Ganesan, Nalinda Somasiri, Rebecca Jeyavadhanam, Gayathri Karthick

Abstract:

The COVID-19 crisis presents a substantial and critical hazard to worldwide health. Since the occurrence of the disease in late January 2020 in the UK, the number of infected people confirmed to acquire the illness has increased tremendously across the country, and the number of individuals affected is undoubtedly considerably high. The purpose of this research is to figure out a predictive machine learning (ML) archetypal that could forecast the COVID-19 cases within the UK. This study concentrates on the statistical data collected from 31st January 2020 to 31st March 2021 in the United Kingdom. Information on total COVID-19 cases registered, new cases encountered on a daily basis, total death registered, and patients’ death per day due to Coronavirus is collected from World Health Organization (WHO). Data preprocessing is carried out to identify any missing values, outliers, or anomalies in the dataset. The data are split into 8:2 ratio for training and testing purposes to forecast future new COVID-19 cases. Support Vector Machine (SVM), Random Forest (RF), and linear regression (LR) algorithms are chosen to study the model performance in the prediction of new COVID-19 cases. From the evaluation metrics such as r-squared value and mean squared error, the statistical performance of the model in predicting the new COVID-19 cases is evaluated. RF outperformed the other two ML algorithms with a training accuracy of 99.47% and testing accuracy of 98.26% when n = 30. The mean square error obtained for RF is 4.05e11, which is lesser compared to the other predictive models used for this study. From the experimental analysis, RF algorithm can perform more effectively and efficiently in predicting the new COVID-19 cases, which could help the health sector to take relevant control measures for the spread of the virus.

Keywords: COVID-19, machine learning, supervised learning, unsupervised learning, linear regression, support vector machine, random forest.

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Authors: Pattrarat Teamkao, Paitip Thiravetyan

Abstract:

The aim of this work was to investigate the potential of soil microorganisms and the burhead plant, as well as the combination of soil microorganisms and plants to remediate monoethylene glycol (MEG), diethylene glycol (DEG), and triethylene glycol (TEG) in synthetic wastewater. The result showed that a system containing both burhead plant and soil microorganisms had the highest efficiency in EGs removal. Around 100% of MEG and DEG and 85% of TEG were removed within 15 days of the experiments. However, the burhead plant had higher removal efficiency than soil microorganisms for MEG and DEG but the same for TEG in the study systems. The removal rate of EGs in the study system related to the molecular weight of the compounds and MEG, the smallest glycol, was removed faster than DEG and TEG by both the burhead plant and soil microorganisms in the study system.

Keywords: Ethylene glycol, burhead plant, soil microorganisms, phytoremediation

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Authors: Marziyeh Halimi, Roushanak Lotfikar, Simin Mansouri Borojeni

Abstract:

In this paper we considered the Neumann problem for the fourth order differential equation. First we define the weighted Sobolev space 2 Wα and generalized solution for this equation. Then we consider the existence and uniqueness of the generalized solution, as well as give the description of the spectrum and of the domain of definition of the corresponding operator.

Keywords: Neumann problem, weighted Sobolev spaces, generalized solution, spectrum of linear operators.2000 mathematic subject classification: 34A05, 34A30.

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Authors: S. Krustev, V. Angelova, K. Ivanov, P. Zaprjanova

Abstract:

It is generally accepted that only about ten microelements are vitally important to all plants, and approximately ten more elements are proved to be significant for the development of some species. The main methods for their determination in soils are the atomic spectral techniques - AAS and ICP-OAS. Critical stage to obtain correct results for content of heavy metals and nutrients in the soil is the process of mineralization. A comparative study of the most widely spread methods for soil sample preparation for determination of some trace elements was carried out. Three most commonly used methods for sample preparation were used as follows: ISO11466, EPA Method 3051 and BDS ISO 14869-1. Their capabilities were assessed and their bounds of applicability in determining the levels of the most important microelements in agriculture were defined.

Keywords: Comparative study, mineralization methods, trace elements.

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Authors: Jing Wu

Abstract:

In this paper, we discuss semiconvergence of the alternating iterative methods for solving singular systems. The semiconvergence theories for the alternating methods are established when the coefficient matrix is a singular matrix. Furthermore, the corresponding comparison theorems are obtained.

Keywords: Alternating iterative method, Semiconvergence, Singular matrix.

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Authors: Adil Al-Rammahi

Abstract:

Laplace transformations have wide applications in engineering and sciences. All previous studies of modified Laplace transformations depend on differential equation with initial conditions. The purpose of our paper is to solve the linear differential equations (not initial value problem) and then find the general solution (not particular) via the Laplace transformations without needed any initial condition. The study involves both types of differential equations, ordinary and partial.

Keywords: Differential Equations, Laplace Transformations.

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