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Improving Numerical Solutions For The Generalized Huxley Equation: The New Iterative Method (Nim), Belal Batiha, Areen Al-Khateeb, Hamzeh Zureigat May 2023

Improving Numerical Solutions For The Generalized Huxley Equation: The New Iterative Method (Nim), Belal Batiha, Areen Al-Khateeb, Hamzeh Zureigat

Applied Mathematics & Information Sciences

The focus of our research was to address the generalized Huxley equation using the recently developed iterative method called the new iterative method (NIM). Our study entailed a comprehensive investigation of the convergence characteristics of the NIM. Additionally, we compared the outcomes obtained from the NIM with other established iterative techniques, including the variational iteration method (VIM) and Adomian decomposition method (ADM), as well as the exact solution.


Some Properties Of Incomplete First Appell Hypergeometric Matrix Functions, Ayed Al E’Damat, Ashish Verma, Jihad Younis, Hassen Aydi May 2023

Some Properties Of Incomplete First Appell Hypergeometric Matrix Functions, Ayed Al E’Damat, Ashish Verma, Jihad Younis, Hassen Aydi

Applied Mathematics & Information Sciences

The aim of this paper to introduce two incomplete first Appell hypergeometric matrix functions (IFAHMFs) γ1 and Γ1 by means of the incomplete Pochhammer matrix symbols. Furthermore, there is a derivation of some results such as integral formula, recursion formula, differentiation formula and finite summation formula of the IFAHMFs γ1 and Γ1.


Application Of Effective Semi-Analytical Algorithms For Neutral And Retarded Volterra Integrodifferential Equations, Mohamed S. M. Bahgat, Mofida Zaki May 2023

Application Of Effective Semi-Analytical Algorithms For Neutral And Retarded Volterra Integrodifferential Equations, Mohamed S. M. Bahgat, Mofida Zaki

Applied Mathematics & Information Sciences

This study developed three semi-analytical algorithms to solve functional integrodifferential equations with variable delays under initial conditions. These algorithms embrace the Laplace Adomian decomposition method (LADM), the modified Laplace Adomian decomposition method (MLADM), and the Laplace variational iteration method (LVIM). Using the suggested approaches, we find the solutions without discretization, transformation, or limiting traditions while considering suitable initial conditions. In addition, the solutions are generated in fast-converging series with easily calculable terms. The proposed methodologies are tested numerically on three numerical applications to prove their efficacy and dependability as well as to compare their computational efficiency. Based on the numerical …


Polar Convex Programming: A New Paradigm For Nonlinear Optimization, Lilia Benakkouche, Blake Whitman, Baha Alzalg May 2023

Polar Convex Programming: A New Paradigm For Nonlinear Optimization, Lilia Benakkouche, Blake Whitman, Baha Alzalg

Applied Mathematics & Information Sciences

In this paper, our central notions of analysis are convexity and betweenness. These concepts are given from the viewpoint of conceptual spaces and are specified in relation to the coordinates of a polar system. We introduce and study a problem that seeks to optimize a polar convex objective subject to polar convex constraints, which we refer to as the polar convex programming problem. We utilize a geometric methodology to solve the two-dimensional version of this optimization problem. Our interpretation of the approach is inspired by the classical graphical method for linear optimization problems. To the best of our knowledge, this …


Solitary Wave Solution For Fractional-Order General Equal-Width Equation Via Semi Analytical Technique, Khalid K. Ali, F. E. Abd Elbary, Mohamed S. Abdel-Wahed, M. A. Elsisy, Mourad S. Semary May 2023

Solitary Wave Solution For Fractional-Order General Equal-Width Equation Via Semi Analytical Technique, Khalid K. Ali, F. E. Abd Elbary, Mohamed S. Abdel-Wahed, M. A. Elsisy, Mourad S. Semary

Applied Mathematics & Information Sciences

This paper presents an innovative approach to solve equal-width time-fractional-order equations that describe the behavior of waves in a certain physical system, using the Caputo operator to express the fractional derivative by improving the Taylor series expansion.Its convergence theorem is proven, and the error between the exact and approximate solutions is estimated; the resulting solutions are illustrated using graphs for different values of the fractional derivative order and time.The primary objective of this study is to demonstrate the effectiveness of the method in reducing computational effort for solving nonlinear fractional partial differential equations (NFPDEs).


Fractional Dynamic Inequalities Of Hardy’S Type On Time Scales, M. R. Kenawy May 2023

Fractional Dynamic Inequalities Of Hardy’S Type On Time Scales, M. R. Kenawy

Applied Mathematics & Information Sciences

In this paper, I obtain some new fractional dynamic inequalities of Hardy and reversed Hardy via time scales. The main outcomes achieved through utilizing inequality of Ho ̈lder and reversed Ho ̈lder on fractional time scales. The inequalities obtained will lead to the classical inequalities which are established earlier.


Adapted Shifted Chebyshevu Operational Matrix Of Derivatives: Two Algorithms For Solving Even-Order Bvps, Dina Abdelhamied, M. Abdelhakem, M. El-Kady, Y. H. Youssri May 2023

Adapted Shifted Chebyshevu Operational Matrix Of Derivatives: Two Algorithms For Solving Even-Order Bvps, Dina Abdelhamied, M. Abdelhakem, M. El-Kady, Y. H. Youssri

Applied Mathematics & Information Sciences

Herein, modified orthogonal polynomials are introduced. These polynomials are generated from the second kind of shifted Chebyshev polynomials on the interval [α, β]. The operational matrix of its derivative is constructed. The Tau and Galerkin method with the proposed orthogonal polynomials is used to solve the boundary value problems (BVPs) with even order. The effectiveness of these methods is proved through their application to several BVPs.


Monotonic And Asymptotic Properties Of Solutions Of Emden-Fowler Neutral Differential Equations And Their Applications, Osama Moaaz, Shatha Qandos, Renad Alqefari, Razan Alrusainy May 2023

Monotonic And Asymptotic Properties Of Solutions Of Emden-Fowler Neutral Differential Equations And Their Applications, Osama Moaaz, Shatha Qandos, Renad Alqefari, Razan Alrusainy

Applied Mathematics & Information Sciences

The objective of this work is to improve the relationships between the solutions of neutral differential equations and their corresponding functions in the classical case. We use these relationships to optimize the conditions that test the oscillation of solutions to Emden-Fowler neutral differential equations. We consider both cases p < 1 and p > 1. In the case p > 1, we test the oscillation of the solutions without imposing the conventional constraints on the delay functions. The approach adopted depends on deducing new properties for the positive solutions of the studied equation, and these properties are of an iterative nature. The iterative nature of properties …


Establishing The Coexistence Of Wolbachia-Carrying And Wild Aedes Aegypti Populations By Feedback Linearization, Antone Dos Santos Benedito, Claudia Pio Ferreira, Helenice De Oliveira Florentino May 2023

Establishing The Coexistence Of Wolbachia-Carrying And Wild Aedes Aegypti Populations By Feedback Linearization, Antone Dos Santos Benedito, Claudia Pio Ferreira, Helenice De Oliveira Florentino

Applied Mathematics & Information Sciences

Wolbachia-based control for the reduction of arboviruses transmitted by Aedes aegypti mosquito is often designed to thoroughly wipe out the wild population replacing it by Wolbachia-carrying individuals. Overall, there has been no focus on plans looking for establishing the coexistence of these populations sharing the same locality. Holding repeated replacement interventions could lead us in a long-term to a possible eradication scenario for this species in its natural state. Nevertheless, annihilating species has been a subject of great controversy and qualms among conservative scientists, since there is no warranty of safeguarding the ecological balance and human welfare. Taking this into …


Pmrsa: Designing An Efficient And Secure Public-Key Similar To Rsa Based On Polynomial Ring, Fatima Rheem Atea, Hassan Rashed Yassein May 2023

Pmrsa: Designing An Efficient And Secure Public-Key Similar To Rsa Based On Polynomial Ring, Fatima Rheem Atea, Hassan Rashed Yassein

Applied Mathematics & Information Sciences

RSA and NTRU encryption methods it is the still used nowadays and they constantly evolving simultaneously, thus paper proposed an encryption method based on linking the concepts of NTRU and modified RSA by using polynomials ring Zp[κ]/ < N (κ) > through generate two public keys, consisting four polynomials private key, this increase increases the complexity algorithm, in spite of this method is slows although this method is slow, it gives a high efficiency of security.


Effects Of Factors On The Market Price Of The Shares Using Design Of Experiment, Amir Ahmad Dar, Mohammad Shahfaraz Khan, Imran Azad, Tanveer Ahmad Tarray, N. Anuradha, Qaiser Farroq Dar May 2023

Effects Of Factors On The Market Price Of The Shares Using Design Of Experiment, Amir Ahmad Dar, Mohammad Shahfaraz Khan, Imran Azad, Tanveer Ahmad Tarray, N. Anuradha, Qaiser Farroq Dar

Applied Mathematics & Information Sciences

When the cost of capital, dividends and the price of the share at the beginning is known, Modigliani and Miller’s model can be used to estimate the price of the share at the end of the period. A design of experiment (Taguchi’s orthogonal array) is used in order to investigate the impact of three parameters on the price of the share at the end of the period. The main aim of this research article is to find which parameter is more significant on the price of the share at the end of the period. Taguchi’s methodology of design of the …


Closed-Form Solutions For Cauchy-Euler Differential Equations Through The New Iterative Method (Nim), Belal Batiha, Ahmed Salem Heila, Firas Ghanim May 2023

Closed-Form Solutions For Cauchy-Euler Differential Equations Through The New Iterative Method (Nim), Belal Batiha, Ahmed Salem Heila, Firas Ghanim

Applied Mathematics & Information Sciences

In this paper, a new iterative method (NIM) is proposed for solving Cauchy-Euler differential equations. NIM simplifies the computational process and directly addresses both linear and nonlinear, homogeneous and non-homogeneous equations, while being user-friendly and accessible. The method’s efficiency, reliability, and accuracy are demonstrated through four examples. NIM offers a versatile and practical solution, making it a valuable tool for mathematical analysis.


Online Education And Managing Service Quality With The Challenges Of Covid 19: The Case Of University Of Business And Technology (Ubt) Saudi Arabia, Mohammad Kanan, Ayman Zerban, Salah Abunar, Ameen El Harbi, Gamal Weheba, Ramiz Assaf Mar 2023

Online Education And Managing Service Quality With The Challenges Of Covid 19: The Case Of University Of Business And Technology (Ubt) Saudi Arabia, Mohammad Kanan, Ayman Zerban, Salah Abunar, Ameen El Harbi, Gamal Weheba, Ramiz Assaf

Applied Mathematics & Information Sciences

With the pandemic of COVID 19 hitting global economy and forcing social distance, all sectors were exposed to the wave. The educational sector is not exceptional, most universities were forced to adopt online education with the lack of experience necessary needed. This step was like walking blind in a foggy road without realizing the suitability of this service or how to satisfy students. The pandemic spread of Novel Corona Virus (COVID-19) has created stress, anxiety, and several concerns among people around the world. It is disrupting every aspect of human life including education. Since customer satisfaction has always been linked …


Semi-Analytical Technique To Study The Dynamics Of Low Earth Satellites Under Gravitational Perturbations Using Universal Variables, A. B. Yassen, A. H. Ibrahim, M. Radwan, W. N. Ahmed Mar 2023

Semi-Analytical Technique To Study The Dynamics Of Low Earth Satellites Under Gravitational Perturbations Using Universal Variables, A. B. Yassen, A. H. Ibrahim, M. Radwan, W. N. Ahmed

Applied Mathematics & Information Sciences

Low-altitude Earth orbits provide important benefits for space missions. Among these benefits are the high-resolution images and resupply. In the present work, we studied the dynamics of Earth satellites that move in low orbits. The force model comprises the gravitational resonance 13:1, besides the Earth’s gravitational potential up to the second degree and order. In order to avoid the appearance of singularities, the quasi-Hamiltonian equations of motion are formulated in terms of non-singular universal variables instead of Delaunay variables. We integrated numerically the equations of motion and performed some numerical simulations. It is found that the variations in eccentricity and …


Some Differential Identities For Rings Involving Prime Ideals, J. J. Jaraden, B. N. Al-Hasanat, L. Oukhtite, I. A. Al-Lawama Mar 2023

Some Differential Identities For Rings Involving Prime Ideals, J. J. Jaraden, B. N. Al-Hasanat, L. Oukhtite, I. A. Al-Lawama

Applied Mathematics & Information Sciences

In many studies on ring structures, derivations are found to play a significant role in determining commutativity. In this paper we show the commutativity of a prime ring using certain identities on the generalized semi-derivation of such ring. The considered derivation maps will be either centralizing or commuting. We intend to propose such results as a new method to demonstrate prime ring commutativity.


Nonmagnetic Negative Refractive Index Media Based On Chalcogenide Glasses, N. Boutabba Mar 2023

Nonmagnetic Negative Refractive Index Media Based On Chalcogenide Glasses, N. Boutabba

Applied Mathematics & Information Sciences

We report in this work the study of the permittivity and the losses in non-linear nonmagnetic negative refractive index media. We analyze the permittivity and the losses dependence on the inclusion number of the particles used in the suggested media that is made by interlacing plasmonic metallic particles and a dielectric. We show that the exhibition of a negative permittivity in these strongly anisotropic media depends not only on the inclusion number of the particles and the frequency range but also on the oscillation frequency of free electrons in the metal which plays the major role. We finally suggest the …


A Preliminary Volterra Lotka Model Analysing Cancer, Intracellular Parasite, And Immune Cells Interaction, Nadia Boutabba, Gehan Abuelenain Mar 2023

A Preliminary Volterra Lotka Model Analysing Cancer, Intracellular Parasite, And Immune Cells Interaction, Nadia Boutabba, Gehan Abuelenain

Applied Mathematics & Information Sciences

In this paper, we investigate the dynamics of immune and tumor cell densities in the presence of a parasite using the prey- predator Volterra-Lotka model in a biological system, assuming that the parasite is either a down or up-regulator of the induced immune cells. Thus, we analysed the model for equal and non equal initial conditions and report their impact on the populations growth.


Ola Distribution: A New One Parameter Model With Applications To Engineering And Covid-19 Data, Ola Al-Ta’Ani, Mohammed M. Gharaibeh Mar 2023

Ola Distribution: A New One Parameter Model With Applications To Engineering And Covid-19 Data, Ola Al-Ta’Ani, Mohammed M. Gharaibeh

Applied Mathematics & Information Sciences

We employed the notion of mixture distributions to suggest a new one parameter continuous distribution for modeling real lifetime data called Ola Distribution. Its properties are explored including moments and related measures, moment generating function, reliability analysis functions, order statistics, Bonferroni and Lorenz curves, stochastic ordering, Re ́nyi entropy and mean deviations. The maximum likelihood method is adapted to estimate the parameter of the distribution. Applications to engineering and COVID- 19 data sets are presented to illustrate the usefulness of the suggested distribution. The applications showed that Ola distribution outperforms some competitive distributions and can be considered as a useful …


Numerical Solution For The Sin-Gordon Equation Using The Finite Difference Method And The Non-Stander Finite Difference Method, K. R. Raslan, A. A. Soliman, Khalid K. Ali, M. Gaber, Soma R. Almhdy Mar 2023

Numerical Solution For The Sin-Gordon Equation Using The Finite Difference Method And The Non-Stander Finite Difference Method, K. R. Raslan, A. A. Soliman, Khalid K. Ali, M. Gaber, Soma R. Almhdy

Applied Mathematics & Information Sciences

In this paper, We study the non-linear sin Gordon equation as a numerical solution using two methods.: the finite differences method and the non-standard finite differences method. A comparison is presented between the numerical results of both methods.The stability of two schemes is conditionally stable.Some tables and figures are presented to illustrate our results.


Predictive Analysis Of Misuse Of Alcohol And Drugs Using Machine Learning Algorithms: The Case Of Using An Imbalanced Dataset From South Africa, Alexander Boateng, Christopher Odoom, Eric Teye Mensah, Sarah Mensah Fobi, Daniel Maposa Mar 2023

Predictive Analysis Of Misuse Of Alcohol And Drugs Using Machine Learning Algorithms: The Case Of Using An Imbalanced Dataset From South Africa, Alexander Boateng, Christopher Odoom, Eric Teye Mensah, Sarah Mensah Fobi, Daniel Maposa

Applied Mathematics & Information Sciences

Drug and alcohol misuse has become a significant global distraction to the development of the youths and future leaders, especially in South Africa. The ideal solution to these unhealthy practices is for institutions, governments, and individuals to put preventive measures such as counselling, sanctions, and fines to help control drug and alcohol misuse. However, it is challenging to know the group of people or individuals engaged in such deteriorating activities by merely monitoring individuals physically. It makes it difficult even to plan the measures to control the issue. Therefore this paper has applied and compared six supervised machine learning algorithms …


E-Learning Innovation In The Institutions Of Jordans Higher Education: A Case Study, Nouh Alhindawi Mar 2023

E-Learning Innovation In The Institutions Of Jordans Higher Education: A Case Study, Nouh Alhindawi

Applied Mathematics & Information Sciences

eLearning has gained widespread popularity in recent years due to its convenience and flexibility. In Jordan, the higher education institutions have embraced e-learning and have implemented various innovations in their e-learning programs, based on a national plan for embedding online learning (full and blended) in the higher education system. These innovations include the use of new technologies and tools, collaboration with industry partners, utilization of Open Educational Resources (OER), incorporation of experiential learning, and implementation of personalized and adaptive learning. These approaches have helped to enhance the quality and effectiveness of e-learning programs, and have ensured that they meet the …


Predicting The Behavior Of Solar Energy In Tulkarm City Using Markov Chains And Fuzzy Markov Chains, Saed Mallak, Mohammad Kanan, Samer Alsadi, Ghadeer Sabbah, Siraj Zahran, Hani Attar Mar 2023

Predicting The Behavior Of Solar Energy In Tulkarm City Using Markov Chains And Fuzzy Markov Chains, Saed Mallak, Mohammad Kanan, Samer Alsadi, Ghadeer Sabbah, Siraj Zahran, Hani Attar

Applied Mathematics & Information Sciences

In this paper, we predict the behavior of solar energy in Tulkarm city, Palestine, using Markov chains and fuzzy Markov chains. Relying on solar radiation data in Tulkarm city during 2013–2016, two models are built that correspond to each season. A year is divided into four seasons, each of which consists of three months. Data from the period 2013–2015 are used to build the models, whereas data from 2016 is compared with the results. The accuracy of the models was better in the summer and winter.


Novel Framework For Selecting Cloud Provider Using Neutrosophic And Modified Gan, Mohammed Attya, Ahmed S. Sakr, H. M. Abdulkader, Faisal Al-Showaikh, M. Kamel El-Sayed Mar 2023

Novel Framework For Selecting Cloud Provider Using Neutrosophic And Modified Gan, Mohammed Attya, Ahmed S. Sakr, H. M. Abdulkader, Faisal Al-Showaikh, M. Kamel El-Sayed

Applied Mathematics & Information Sciences

Cloud computing is very important for many companies in the process of progress. The main problem for any company when transferring their work to the cloud is selecting the most suitable cloud provider among the availability of different cloud service providers with different properties and different alternatives. This paper introduces a novel framework that can be used for selecting the most suitable provider in the case of missing values in the evaluation of alternatives. The framework is composed of two steps; the first step in the framework is about using the Modified Generative Adversarial Network (M-GAN) for data imputation of …


Automated Classification Of The Sybil Attack In Blockchain Network Using Multi Neural Memory Network Classifier, D. Nancy Kirupanithi, A. Antonidoss, G. Subathra Mar 2023

Automated Classification Of The Sybil Attack In Blockchain Network Using Multi Neural Memory Network Classifier, D. Nancy Kirupanithi, A. Antonidoss, G. Subathra

Applied Mathematics & Information Sciences

Block chain technology is a distributed form of digital record that does not need any central authority. As all the information available in the block chain are transparent, everyone can see it. Since blockchain technology is almost hack-proof, it has attracted several industries like business, academia, government, and healthcare. Common concerns regarding Blockchain technology’s impact on privacy and security are unfounded, and may be attacked in a number of ways. We discovered that the Sybil attack has a significant effect on public/permissionless blockchains because an attacker may undermine the blockchain by generating a large number of pseudonymous identities (i.e. Fake …


Maximum Symmetric Division Deg Index Of Cactus Graphs With A Fixed Number Of Cycles And Order, Abeer M. Albalahi Mar 2023

Maximum Symmetric Division Deg Index Of Cactus Graphs With A Fixed Number Of Cycles And Order, Abeer M. Albalahi

Applied Mathematics & Information Sciences

The symmetric division deg (SDD) index of a graph G is the addition of the numbers (dvdu)−1[(dv)2 +(du)2] over all the edges uv of G, where dv and du represent degrees of the vertices v and u, respectively. A connected graph in which every edge lies on at most one cycle is usually referred to as a cactus graph. (Every tree as well as every unicyclic graph is a cactus graph; the converse is not generally true.) The primary goal of the present paper is to characterize the unique graph possessing the maximum value of the SDD index over the …


Fuzzy Contra Gprw-Continuous Mappings, Firdose Habib, Ali Akgu ̈L, Abdulrahman M. Alansari, Wasan Shakir Awad Mar 2023

Fuzzy Contra Gprw-Continuous Mappings, Firdose Habib, Ali Akgu ̈L, Abdulrahman M. Alansari, Wasan Shakir Awad

Applied Mathematics & Information Sciences

t: In this manuscript new types of fuzzy mappings namely fuzzy contra gprw-continuous mappings have been introduced & investigated. Also we found out its relation with various other fuzzy contra mappings introduced earlier. We also introduced fuzzy contra gprw-open mappings and fuzzy contra gprw-closed mappings in this paper.


On The Robustness Of Right Truncated Esscher Transformed Laplace Distribution, K. Krishnakumari, D. George Mar 2023

On The Robustness Of Right Truncated Esscher Transformed Laplace Distribution, K. Krishnakumari, D. George

Applied Mathematics & Information Sciences

Truncation arises in many practical situations such as Epidemiology, Material science, Psychology, Social Sciences and Statistics where one wants to study about data which lie above or below a certain threshold or within a specified range. Right truncation often happens when an event/source is detected if its measurement is less than a truncation variable. The present study aims to introduce a right truncated version of an asymmetric and heavy tailed distribution namely, Esscher transformed Laplace distribution beyond the interval (−∞,b). Various distributional and reliability properties of the proposed distribution are investigated. The performance of η, the parameter, is estimated using …


Survey On Linear Integral Equations And The Laguerre Polynomials, Muhammad Hakim Ali Qasmi, Ali Hasan, Ali Akgu ̈L, Muhammad Farman, Salem M. Aljazzar, Faisal Al-Showaikh Mar 2023

Survey On Linear Integral Equations And The Laguerre Polynomials, Muhammad Hakim Ali Qasmi, Ali Hasan, Ali Akgu ̈L, Muhammad Farman, Salem M. Aljazzar, Faisal Al-Showaikh

Applied Mathematics & Information Sciences

In this paper, we dealt with Integral Equations (IEs). Many real-world problems are modeled in the form of IEs. Nowadays, IEs are used frequently as a replacement for Differential Equations. There are various methods to deal with IEs such as ADM, VIM, and HPM, etc. Here in this work, we used Galerkin Method. In this method, we considered Laguerre Polynomials (some other polynomials may also be used). In the method, the Galerkin equation is solved by using Maple Code for getting unknown constants, solutions, and Graphs.


Fractional Order Glucose Insulin Model With Generalized Mittag-Leffler Kernel, Ali Akgül, Muhammad Farman, Aqeel Ahmad, Adnan Khan, Siraj Zahran, Wasan Shakir Awad Mar 2023

Fractional Order Glucose Insulin Model With Generalized Mittag-Leffler Kernel, Ali Akgül, Muhammad Farman, Aqeel Ahmad, Adnan Khan, Siraj Zahran, Wasan Shakir Awad

Applied Mathematics & Information Sciences

In this paper, We formulate a fractional-order mathematical model for the populations of diabetic patients consist three- compartment G, X, and I. Diabetes Model is investigated with fractal-fractional operator for normal and type-1 diabetes. Also, the deterministic mathematical model for diabetes mellitus is investigated with the effect of the fractional parameters. Solutions are derived to investigate the influence of fractional operator which shows the impact of the disease for type-1 diabetes. The existence and uniqueness results of the fractional-order model are derived using fixed point theory. Simulation has been made for developed solutions of fractional order diabetes model to check …


Fast Facial Expression Recognition System: Selection Of Models, L. Atymtayeva, M. Kanatov, A. M. A Musleh, G. Tulemissova Mar 2023

Fast Facial Expression Recognition System: Selection Of Models, L. Atymtayeva, M. Kanatov, A. M. A Musleh, G. Tulemissova

Applied Mathematics & Information Sciences

Facial Expression Recognition (FER) is rapidly developing field of Computer Vision and Pattern Recognition directions. FER can be helpful for various purposes: in security systems for aggression recognition, in education for students interests recognition, in marketing for customer satisfaction and in the many other fields. Usually we can distinguish seven common facial expressions for all persons. However, it is often important to know: whether a person is positive or negative. This paper describes the recognition system for facial expression in real time, which defines relatively fast and accurate the positive or negative emotion of the faces in the camera view …