Search results for: asymmetric nonlinear model

Authors: Abdullah Eqal Al Mazrooei

Abstract:

In this work, a new nonlinear model will be introduced. The model is in the state-space form. The nonlinearity of this model is in the state equation where the state vector is multiplied by its self. This technique makes our model generalizes many famous models as Lotka-Volterra model and Lorenz model which have many applications in the real life. We will apply our new model to estimate the wind speed by using a new nonlinear estimator which suitable to work with our model.

Keywords: nonlinear systems, state-space model, Kronecker product, nonlinear estimator

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Authors: Qaiser Munir, Hamid Hussain

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Oil prices are believed to have a major impact on several economic indicators, leading to several instances where a comparison between oil prices and a trade deficit of oil-importing countries have been carried out. Building upon the narrative, this paper sheds light on the ongoing debate by inquiring upon the possibility of asymmetric linkages between oil prices, industrial production, exchange rate, whole price index, and trade deficit. The analytical tool used to further understand the complexities of a recent approach called nonlinear auto-regressive distributed lag model (NARDL) is utilised. Our results suggest that there are significant asymmetric effects among the main variables of interest. Further, our findings indicate that any variation in oil prices, industrial production, exchange rate, and whole price index on trade deficit tend to fluctuate in the long run. Moreover, the long-run picture denotes that increased oil price leads to a negative impact on the trade deficit, which, in its true essence, is a disproportionate impact. In addition to this, the Wald test simultaneously conducted concludes the absence of any significant evidence of the asymmetry in the oil prices impact on the trade balance in the short-run.

Keywords: trade deficit, oil prices, developing economy, NARDL

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Authors: Farrukh Javed, Krzysztof Podgórski

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We propose a new model that accounts for the asymmetric response of volatility to positive ('good news') and negative ('bad news') shocks in economic time series the so-called leverage effect. In the past, asymmetric powers of errors in the conditionally heteroskedastic models have been used to capture this effect. Our model is using the gamma difference representation of the generalized Laplace distributions that efficiently models the asymmetry. It has one additional natural parameter, the shape, that is used instead of power in the asymmetric power models to capture the strength of a long-lasting effect of shocks. Some fundamental properties of the model are provided including the formula for covariances and an explicit form for the conditional distribution of 'bad' and 'good' news processes given the past the property that is important for the statistical fitting of the model. Relevant features of volatility models are illustrated using S&P 500 historical data.

Keywords: heavy tails, volatility clustering, generalized asymmetric laplace distribution, leverage effect, conditional heteroskedasticity, asymmetric power volatility, GARCH models

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Authors: Nabilah Ibrahim, Hafiz Mohd Zaini, Wan Fatin Liyana Mutalib

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Ultrasound equipment or machine is capable to scan in two dimensional (2D) areas. However there are some limitations occur during scanning an object. The problem will occur when scanning process that involving the asymmetric object. In this project, the ultrasound probe holder for asymmetric reflector scanning in 3D image is proposed to make easier for scanning the phantom or object that has asymmetric shape. Initially, the constructed asymmetric phantom that construct will be used in 2D scanning. Next, the asymmetric phantom will be interfaced by the movement of ultrasound probe holder using the Arduino software. After that, the performance of the ultrasound probe holder will be evaluated by using the various asymmetric reflector or phantom in constructing a 3D image

Keywords: ultrasound 3D images, axial and lateral resolution, asymmetric reflector, Arduino software

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Authors: Minas Balyan

Abstract:

Nowadays X-ray nonlinear diffraction and nonlinear effects are investigated due to the presence of the third generation synchrotron sources and XFELs. X-ray third order nonlinear dynamical diffraction is considered as well. Using the nonlinear model of the usual visible light optics the third-order nonlinear Takagi’s equations for monochromatic waves and the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses are obtained by the author in previous papers. The obtained equations show, that even if the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero (forbidden reflection), the dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus, in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well-known Renninger effect takes place. In this work, the 'third order nonlinear Renninger effect' is considered theoretically.

Keywords: Bragg diffraction, nonlinear Takagi’s equations, nonlinear Renninger effect, third order nonlinearity

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Authors: Alexander Pesin, Denis Pustovoytov, Mikhail Sverdlik

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Materials with ultrafine-grained structure and unique physical and mechanical properties can be obtained by methods of severe plastic deformation, which include processes of asymmetric rolling (AR). Asymmetric rolling is a very effective way to create ultrafine-grained structures of metals and alloys. Since the asymmetric rolling is a continuous process, it has great potential for industrial production of ultrafine-grained structure sheets. Basic principles of asymmetric rolling are described in detail in scientific literature. In this work finite element modeling of asymmetric rolling and metal forming processes in multiroll gauge was performed. Parameters of the processes which allow achieving significant values of shear strain were defined. The results of the study will be useful for the research of the evolution of ultra-fine metal structure in asymmetric rolling.

Keywords: asymmetric rolling, equivalent strain, FEM, multiroll gauge, profile, severe plastic deformation, shear strain, sheet

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Authors: Ahmad Akrad, Rabia Sehab, Fadi Alyoussef

Abstract:

Nowadays, induction machines are widely used in industry thankful to their advantages comparing to other technologies. Indeed, there is a big demand because of their reliability, robustness and cost. The objective of this paper is to deal with diagnosis, detection and isolation of faults in a three-phase induction machine. Among the faults, Inter-turn short-circuit fault (ITSC), current sensors fault and single-phase open circuit fault are selected to deal with. However, a fault detection method is suggested using residual errors generated by the root mean square (RMS) of phase currents. The application of this method is based on an asymmetric nonlinear model of Induction Machine considering the winding fault of the three axes frame state space. In addition, current sensor redundancy and sensor fault detection and isolation (FDI) are adopted to ensure safety operation of induction machine drive. Finally, a validation is carried out by simulation in healthy and faulty operation modes to show the benefit of the proposed method to detect and to locate with, a high reliability, the three types of faults.

Keywords: induction machine, asymmetric nonlinear model, fault diagnosis, inter-turn short-circuit fault, root mean square, current sensor fault, fault detection and isolation

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Authors: Doğan Yıldız, Aydan Müşerref Erkmen

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The controller of the octocopter is mostly based on the PID controller. For complex maneuvers, PID controllers have limited performance capability like in collision avoidance. When an octocopter needs avoidance from an obstacle, it must instantly show an agile maneuver. Also, this kind of maneuver is affected severely by the nonlinear characteristic of octocopter. When these kinds of limitations are considered, the situation is highly challenging for the PID controller. In the proposed study, these challenges are tried to minimize by using the model predictive controller (MPC) for collision avoidance with a nonlinear octocopter model. The aim is to show that MPC-based collision avoidance has the capability to deal with fast varying conditions in case of obstacle detection and diminish the nonlinear effects of octocopter with varying disturbances.

Keywords: model predictive control, nonlinear octocopter model, collision avoidance, obstacle detection

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Authors: Abdullah Eqal Al Mazrooei

Abstract:

Kalman filter is a famous algorithm that utilizes to estimate the state in the linear systems. It has numerous applications in technology and science. Since of the most of applications in real life can be described by nonlinear systems. So, Kalman filter does not work with the nonlinear systems because it is suitable to linear systems only. In this work, a nonlinear filtering algorithm is presented which is suitable to use with the special kinds of nonlinear systems. This filter generalizes the Kalman filter. This means that this filter also can be used for the linear systems. Our algorithm depends on a special linearization of the second degree. We introduced the nonlinear algorithm with a bilinear state-space model. A simulation example is presented to illustrate the efficiency of the algorithm.

Keywords: Kalman filter, filtering algorithm, nonlinear systems, state-space model

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Authors: Nicolò Vaiana, Giorgio Serino

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The nonlinear time history analysis of seismically base-isolated structures can require a significant computational effort when the behavior of each seismic isolator is predicted by adopting the widely used differential equation Bouc-Wen model. In this paper, a nonlinear exponential model, able to simulate the response of seismic isolation bearings within a relatively large displacements range, is described and adopted in order to reduce the numerical computations and speed up the nonlinear dynamic analysis. Compared to the Bouc-Wen model, the proposed one does not require the numerical solution of a nonlinear differential equation for each time step of the analysis. The seismic response of a 3d base-isolated structure with a lead rubber bearing system subjected to harmonic earthquake excitation is simulated by modeling each isolator using the proposed analytical model. The comparison of the numerical results and computational time with those obtained by modeling the lead rubber bearings using the Bouc-Wen model demonstrates the good accuracy of the proposed model and its capability to reduce significantly the computational effort of the analysis.

Keywords: base isolation, computational efficiency, nonlinear exponential model, nonlinear time history analysis

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Authors: Win Ko Ko, A. N. Temnov

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The problem of nonlinear oscillations of a two-layer liquid completely filling a limited volume is considered. Using two basic asymmetric harmonics excited in two mutually perpendicular planes, ordinary differential equations of nonlinear oscillations of the interface of a two-layer liquid are investigated. In this paper, hydrodynamic coefficients of linear and nonlinear problems in integral relations were determined. As a result, the instability regions of forced oscillations of a two-layered liquid in a cylindrical tank occurring in the plane of action of the disturbing force are constructed, as well as the dynamic instability regions of the parametric resonance for different ratios of densities of the upper and lower liquids depending on the amplitudes of liquids from the excitations frequencies. Steady-state regimes of fluid motion were found in the regions of dynamic instability of the initial oscillation form. The Bubnov-Galerkin method is used to construct instability regions for approximate solution of nonlinear differential equations.

Keywords: nonlinear oscillations, two-layered liquid, instability region, hydrodynamic coefficients, resonance frequency

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Authors: Qing Wu, Fei-Yan Li, Heng-Chang Zhang

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Multitask learning support vector machines (SVMs) have recently attracted increasing research attention. Given several related tasks, the single-task learning methods trains each task separately and ignore the inner cross-relationship among tasks. However, multitask learning can capture the correlation information among tasks and achieve better performance by training all tasks simultaneously. In addition, the asymmetric squared loss function can better improve the generalization ability of the models on the most asymmetric distributed data. In this paper, we first make two assumptions on the relatedness among tasks and propose two multitask learning proximal support vector machine algorithms, named MTL-a-PSVM and EMTL-a-PSVM, respectively. MTL-a-PSVM seeks a trade-off between the maximum expectile distance for each task model and the closeness of each task model to the general model. As an extension of the MTL-a-PSVM, EMTL-a-PSVM can select appropriate kernel functions for shared information and private information. Besides, two corresponding special cases named MTL-PSVM and EMTLPSVM are proposed by analyzing the asymmetric squared loss function, which can be easily implemented by solving linear systems. Experimental analysis of three classification datasets demonstrates the effectiveness and superiority of our proposed multitask learning algorithms.

Keywords: multitask learning, asymmetric squared loss, EMTL-a-PSVM, classification

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Authors: Shan-Jen Cheng, Te-Jen Chang, Kuang-Hsiung Tan, Shou-Ling Kuo

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Polymer Electrolyte Membrane Fuel Cell (PEMFC) is such a time-vary nonlinear dynamic system. The traditional linear modeling approach is hard to estimate structure correctly of PEMFC system. From this reason, this paper presents a nonlinear modeling of the PEMFC using Neural Network Auto-regressive model with eXogenous inputs (NNARX) approach. The multilayer perception (MLP) network is applied to evaluate the structure of the NNARX model of PEMFC. The validity and accuracy of NNARX model are tested by one step ahead relating output voltage to input current from measured experimental of PEMFC. The results show that the obtained nonlinear NNARX model can efficiently approximate the dynamic mode of the PEMFC and model output and system measured output consistently.

Keywords: PEMFC, neural network, nonlinear modeling, NNARX

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Authors: Farid Habibi Tanha, Hawati Janor, Mojtaba Jahanbazi

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The purpose of this study is to examine the effect of asymmetric information on the composition of capital inflows. This study uses the stock market microstructure to capture the asymmetric information. Such an approach allows one to capture the level and extent of the asymmetric information from a firm’s perspective. This study focuses on the two-dimensional measure of the market microstructure in capturing asymmetric information. The composition of capital inflows is measured by running six models simultaneously. By employing the panel data technique, the main finding of this research shows an increase in the asymmetric information of the stock market, in any of the two dimensions of width and depth. This leads to the reduction of foreign investments in both forms of foreign portfolio investment (FPI) and foreign direct investment (FDI), while the reduction in FPI is higher than that of the FDI. The significant effect of asymmetric information on capital inflows implicitly suggests for policymakers to control the changes of foreign capital inflows through transparency in the level of the market.

Keywords: capital flows composition, asymmetric information, stock market microstructure, foreign portfolio investment, foreign direct investment

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Authors: Osamu Komori, Shinto Eguchi, Hiroshi Okamura, Momoko Ichinokawa

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The long time-series data on population assessments are essential for global ecosystem assessment because the temporal change of biomass in such a database reflects the status of global ecosystem properly. However, the available assessment data usually have limited sample sizes and the ratio of populations with low abundance of biomass (collapsed) to those with high abundance (non-collapsed) is highly imbalanced. To allow for the imbalance and uncertainty involved in the ecological data, we propose a binary regression model with mixed effects for inferring ecosystem status through an asymmetric logistic model. In the estimation equation, we observe that the weights for the non-collapsed populations are relatively reduced, which in turn puts more importance on the small number of observations of collapsed populations. Moreover, we extend the asymmetric logistic regression model using propensity score to allow for the sample biases observed in the labeled and unlabeled datasets. It robustified the estimation procedure and improved the model fitting.

Keywords: double robust estimation, ecological binary data, mixed effect logistic regression model, propensity score

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Authors: Fernando P. Silva, Valter J. S. Leite, Erivelton G. Nepomuceno

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In this paper, a nonlinear controller design for an omnidirectional mobile is presented. The robot controller consists of an inner-loop controller and an outer-loop controller, the first is designed using state feedback (robust allocation) and the second controller is designed based on Robust Multi Inversion (RMI) approach. The objective of RMI controller is rendering the robust inversion of the dynamic, when the model is affected by uncertainties. A model nonlinear MIMO of an omni-directional robot (small-league of Robocup) is used to simulate the RMI approach. The parameters of linear and nonlinear model are varied to cause modelling uncertainties among the model and the real model (real system) generating an error in inner-loop controller signal that must be compensated by RMI controller. The simulation test results show that the RMI is capable of compensating the uncertainties and keep the system stable and controlled under uncertainties.

Keywords: robust multi inversion, omni-directional robot, robocup, nonlinear control

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Authors: H. Triki, Y. Hamaizi, A. El-Akrmi

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We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects.

Keywords: nonlinear Schrödinger equation, high-order effects, soliton solution

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Authors: Hsueh-Cheng Yang

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The generation and design of compound involute spur gearings can be used in gear pump. A compound rack cutter with asymmetric involute teeth is presented for determining the mathematical model of compound gear pumps. This paper covers the following topics: (a) generation and geometry of compound rack cutter is presented and used to generate a compound gear and a compound pinion. (b) Based on the developed compound gears, stress analysis was performed for the symmetric gears and the asymmetric gears. Comparing the results of the stress analysis for the asymmetric involute teeth is superior to the symmetric involute teeth. A numerical example that illustrates the developed compound rack cutter is represented.

Keywords: compound, involute teeth, gear pump, rack cutter

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Authors: Hao Chen, Bo Guo, Ping Jiang

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Residual life (RL) estimation based on multi-phase nonlinear Wiener process was studied in this paper, which is significant for complicated products with small samples. Firstly, nonlinear Wiener model with random parameter was introduced and multi-phase nonlinear Wiener model was proposed to model degradation process of products that were nonlinear and separated into different phases. Then the multi-phase RL probability density function based on the presented model was derived approximately in a closed form and parameters estimation was achieved with the method of maximum likelihood estimation (MLE). Finally, the method was applied to estimate the RL of high voltage plus capacitor. Compared with the other three different models by log-likelihood function (Log-LF) and Akaike information criterion (AIC), the results show that the proposed degradation model can capture degradation process of high voltage plus capacitors in a better way and provide a more reliable result.

Keywords: multi-phase nonlinear wiener process, residual life estimation, maximum likelihood estimation, high voltage plus capacitor

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Authors: Ward Brullot, Thierry Verbiest

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Nonreciprocal optical effects, such as Faraday rotation or magnetic circular dichroism, are very useful both for fundamental studies as for applications such as magnetic field sensors or optical isolators. In this study, we developed layer-by-layer deposited 20nm thick plasmonic nanoparticle aggregates consisting of gold, silver and magnetite nanoparticles that show broadband nonreciprocal asymmetric transmission. As such, the optical transmittance, or absorbance, depends on the direction of light propagation in the material, which means that looking from one direction or the other, more or less light passes through the sample. Theoretical analysis showed that strong electric quadrupole fields, which are electric field gradients, occur in the aggregates and that these quadrupole fields are responsible for the observed asymmetric transmission and the nonreciprocity of the effect. Apart from nonreciprocal asymmetric transmission, also other effects such as, but not limited to, optical rotation, circular dichroism or nonlinear optical responses were measured in the plasmonic nanoparticle aggregates and the influences of the intense electric quadrupole fields determined. In conclusion, the presence of strong electric quadrupole fields make the developed plasmonic nanoparticle aggregates ideal candidates for the study and application of various nonreciprocal optical effects.

Keywords: asymmetric transmission, electric quadrupoles, nanoparticle aggregates, nonreciprocity

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Authors: Serpil Türkyılmaz, Mesut Balıbey

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In this study, long memory properties in volatility of Turkey Stock Market are being examined through the FIGARCH, FIEGARCH and FIAPARCH models under different distribution assumptions as normal and skewed student-t distributions. Furthermore, structural changes in volatility of Turkey Stock Market are investigated. The results display long memory property and the presence of asymmetric effects of shocks in volatility of Turkey Stock Market.

Keywords: FIAPARCH model, FIEGARCH model, FIGARCH model, structural break

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Authors: Kanica Goel, Nilam

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Infectious diseases are a leading cause of death worldwide and hence a great challenge for every nation. Thus, it becomes utmost essential to prevent and reduce the spread of infectious disease among humans. Mathematical models help to better understand the transmission dynamics and spread of infections. For this purpose, in the present article, we have proposed a nonlinear time-delayed SVIRS (Susceptible-Vaccinated-Infected-Recovered-Susceptible) mathematical model with nonlinear type incidence rate and nonlinear type treatment rate. Analytical study of the model shows that model exhibits two types of equilibrium points, namely, disease-free equilibrium and endemic equilibrium. Further, for the long-term behavior of the model, stability of the model is discussed with the help of basic reproduction number R₀ and we showed that disease-free equilibrium is locally asymptotically stable if the basic reproduction number R₀ is less than one and unstable if the basic reproduction number R₀ is greater than one for the time lag τ≥0. Furthermore, when basic reproduction number R₀ is one, using center manifold theory and Casillo-Chavez and Song theorem, we showed that the model undergoes transcritical bifurcation. Moreover, numerical simulations are being carried out using MATLAB 2012b to illustrate the theoretical results.

Keywords: nonlinear incidence rate, nonlinear treatment rate, stability, time delayed SVIRS epidemic model

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Authors: A. Giniatoulline

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A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid

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Authors: Jaroslav Krutil, Simona Fialová, , František Pochylý

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A nonlinear mathematical model of mutual fluid-structure interaction is presented in the work. The model is applicable to the general shape of sealing gaps. An in compressible fluid and turbulent flow is assumed. The shaft carries a rotational and procession motion, the gap is axially flowed through. The achieved results of the additional mass, damping and stiffness matrices may be used in the solution of the rotor dynamics. The usage of this mathematical model is expected particularly in hydraulic machines. The method of control volumes in the ANSYS Fluent was used for the simulation. The obtained results of the pressure and velocity fields are used in the mathematical model of additional effects.

Keywords: nonlinear mathematical model, CFD modeling, hydrodynamic sealing gap, matrices of mass, stiffness, damping

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Authors: Maba Boniface Matadi

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This paper analyses the model of Malaria endemic from the point of view of the group theoretic approach. The study identified new independent variables that lead to the transformation of the nonlinear model. Furthermore, corresponding determining equations were constructed, and new symmetries were found. As a result, the findings of the study demonstrate of the integrability of the model to present an invariant solution for the Malaria model.

Keywords: group theory, lie symmetry, invariant solutions, malaria

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Authors: Bououden Soraya

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This paper aims to study the existence of the change of coordinates which permits to transform a class of nonlinear dynamical systems into the so-called nonlinear observer canonical form (NOCF). Moreover, an algorithm to construct such a change of coordinates is given. Based on this form, we can design an observer with a linear error dynamic. This enables us to estimate the state of a nonlinear dynamical system. A concrete example (biological model) is provided to illustrate the feasibility of the proposed results.

Keywords: nonlinear observer canonical form, observer, design, gene regulation, gene expression

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Authors: Shahrokh Barati

Abstract:

In this paper, we introduced AIDS disease at first, then proposed dynamic model illustrate its progress, after expression of a short history of nonlinear modeling by polynomial phasing systems, we considered the stability conditions of the systems, which contained a huge amount of researches in order to modeling and control of AIDS in dynamic nonlinear form, in this approach using a frame work of control any polynomial phasing modeling system which have been generalized by part of phasing model of T-S, in order to control the system in better way, the stability conditions were achieved based on polynomial functions, then we focused to design the appropriate controller, firstly we considered the equilibrium points of system and their conditions and in order to examine changes in the parameters, we presented polynomial phase model that was the generalized approach rather than previous Takagi Sugeno models, then with using case we evaluated the equations in both open loop and close loop and with helping the controlling feedback, the close loop equations of system were calculated, to simulate nonlinear model of AIDS disease, we used polynomial phasing controller output that was capable to make the parameters of a nonlinear system to follow a sustainable reference model properly.

Keywords: polynomial fuzzy, AIDS, nonlinear AIDS model, fuzzy control systems

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Authors: Tudor Barbu

Abstract:

We present a robust nonlinear parabolic partial differential equation (PDE)-based denoising scheme in this article. Our approach is based on a second-order anisotropic diffusion model that is described first. Then, a consistent and explicit numerical approximation algorithm is constructed for this continuous model by using the finite-difference method. Finally, our restoration experiments and method comparison, which prove the effectiveness of this proposed technique, are discussed in this paper.

Keywords: anisotropic diffusion, finite differences, image denoising and restoration, nonlinear PDE model, anisotropic diffusion, numerical approximation schemes

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Authors: Meriem Mossaddek, El Mehdi Laadissi, El Mehdi Loualid, Chouaib Ennawaoui, Sohaib Bouzaid, Abdelowahed Hajjaji

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An electrochemical system is a subset of mechatronic systems that includes a wide variety of batteries and nickel-cadmium, lead-acid batteries, and lithium-ion. Those structures have several non-linear behaviors and uncertainties in their running range. This paper studies an effective technique for modeling Lithium-Ion (Li-Ion) batteries using a Nonlinear Auto-Regressive model with exogenous input (NARX). The Artificial Neural Network (ANN) is trained to employ the data collected from the battery testing process. The proposed model is implemented on a Li-Ion battery cell. Simulation of this model in MATLAB shows good accuracy of the proposed model.

Keywords: lithium-ion battery, neural network, energy storage, battery model, nonlinear models

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Authors: Sartaj Singh, Amar Singh, Ashok Sharma, Sandeep Kaur

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With upcoming threats in a digital world, we need to work continuously in the area of security in all aspects, from hardware to software as well as data modelling. The rise in social media activities and hunger for data by various entities leads to cybercrime and more attack on the privacy and security of persons. Cryptography has always been employed to avoid access to important data by using many processes. Symmetric key and asymmetric key cryptography have been used for keeping data secrets at rest as well in transmission mode. Various cryptosystems have evolved from time to time to make the data more secure. In this research article, we are studying various cryptosystems in asymmetric cryptography and their application with usefulness, and much emphasis is given to Elliptic curve cryptography involving algebraic mathematics.

Keywords: cryptography, symmetric key cryptography, asymmetric key cryptography

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