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The Effect Of Realistic Mathematics Education On Undergraduate Freshmen Students’ Mathematical Competencies, Sarah Omar M. Melaibari, Norulhuda Ismail
The Effect Of Realistic Mathematics Education On Undergraduate Freshmen Students’ Mathematical Competencies, Sarah Omar M. Melaibari, Norulhuda Ismail
Applied Mathematics & Information Sciences
One of the ultimate objectives of the Saudi Vision 2030 is to reduce the country’s dependence on the oil industry and construct a competitive, knowledge-based economy through developing the education system. Mathematics is the base of all scientific disciplines and technology. The recent trends of mathematics education reform have been shifted internationally towards mathematical competencies. This study aims to improve undergraduate freshmen students’ mathematical thinking, reasoning, representation, and handling mathematical symbols and formalism competencies through the implementation of the ”Realistic Mathematics Education” learning strategy. An RME-based pre-calculus course has been implemented in a six-week quasi-experiment involving a total of 39 …
Reinforcement Learning Based Energy Consolidation Model For Efficient Cloud Computing System, B. Prabha, J. Thangakumar, K. Ramesh
Reinforcement Learning Based Energy Consolidation Model For Efficient Cloud Computing System, B. Prabha, J. Thangakumar, K. Ramesh
Applied Mathematics & Information Sciences
Cloud computing offers significant deployment services to the end-users by using various network & software resources which consumes enormous energy. Energy plays a key factor in the ubiquitous cloud system because it involves financial investment for the hardware infrastructure and also contributes for service quality. There are numerous models available the consumption of cloud data center energy. In the prevailing cloud models certain count of resources were experimented which are not providing significant energy consumption due to wide set of applications actively running in the data center. One of the classifications of Machine Learning model is Reinforcement Learning (RL) model …
On Bessel-Maitland Function And M-Parameter Mittag-Leffler Function Associated With Fractional Calculus Operators And Its Applications, Rupakshi Mishra Pandey, Ankita Chandola, Ritu Agarwal
On Bessel-Maitland Function And M-Parameter Mittag-Leffler Function Associated With Fractional Calculus Operators And Its Applications, Rupakshi Mishra Pandey, Ankita Chandola, Ritu Agarwal
Applied Mathematics & Information Sciences
Fractional calculus is of utmost importance because of its extensive use in various fields of inequality theory, applied mathematics, science and engineering. In this paper, our aim is to discuss some image formulas involving various fractional operators that has kernel as the Appell function and the Saigo operators with Bessel-Maitland function and m-parameter Mittag-Leffler function. The results are then represented in the form of the generalized Wright-hypergeometric function. Further, some special and particular cases involving the Mittag-Leffler function, the Wiman function, the Prabhakar function among other generalizations of the Mittag- Leffler function are induced.
Mathematical Modeling Of A Bimodal Pneumonia Epidemic With Non-Breastfeeding Class, Fekadu Mosisa Legesse, Koya Purnachandra Rao, Temesgen Duressa Keno
Mathematical Modeling Of A Bimodal Pneumonia Epidemic With Non-Breastfeeding Class, Fekadu Mosisa Legesse, Koya Purnachandra Rao, Temesgen Duressa Keno
Applied Mathematics & Information Sciences
The world health organization (WHO) recommends breastfeeding is mandatory for two years. To support this recommendation several research work have been done to suggest that breastfeeding has clear advantages, specially in eradicating morbidity and mortality due to infectious diseases like pneumonia in childhood. Having these in consideration this work divides the susceptible individuals in to two different classes depending on the level of adequate nutrition particularly breastfeeding to study the transmission dynamics of Pneumonia. In addition the effect of hygiene care for children under five years is considered. The aim of this work is to examine the effect of breastfeeding …
Statistical Inference Of Modified Frechet–Exponential Distribution With Applications To Real-Life Data, Ahmed T. Farhat, Dina A. Ramadan, B. S. El-Desouky
Statistical Inference Of Modified Frechet–Exponential Distribution With Applications To Real-Life Data, Ahmed T. Farhat, Dina A. Ramadan, B. S. El-Desouky
Applied Mathematics & Information Sciences
This paper introduces a new lifetime model, referred to as modified Frechet–Exponential distribution (MFED), is developed on the basis of the modified Frechet method. Numerous statistical properties of the suggested model are derived and discussed including ordinary and incomplete moments, quantile, mode, the moment generating functions, reliability and order statistics. The observed Fisher’s information matrix is provided, and the model parameters are estimated using the maximum likelihood technique. The suggested model is very adaptable and has the capacity to simulate datasets with monotonic and nonmonotonic failure rates. The proposed model is applied on three real datasets for checking its performance …
Two-Term Trace Estimates For Gradually Successive Relativistic Stable Processes, A. Ali H. Al-Rabiaa, S. Hussein
Two-Term Trace Estimates For Gradually Successive Relativistic Stable Processes, A. Ali H. Al-Rabiaa, S. Hussein
Applied Mathematics & Information Sciences
The current study aims at showing trace estimates, following the way of the method proved by Rodrigo Ba?uelos, Jebessa B. Mijena and Erkan Nane [1] for the relativistic (1+𝜖)-stable process extending the result of Ba?uelos, and Kulczycki [2] in the stable case.
Rough Sets Theory Based Approach For Predicting Students ́ Performance In E-Learning Systems, Manasik M. Nour, Sumayyah I. Alshber, H. A.Mohamed
Rough Sets Theory Based Approach For Predicting Students ́ Performance In E-Learning Systems, Manasik M. Nour, Sumayyah I. Alshber, H. A.Mohamed
Applied Mathematics & Information Sciences
In the recent days, educational data mining Strategies have captured the notice of Scientists according to the rapid growth of educational data and the need for developing methods to discover the hidden knowledge to predict the success of students’ learning. Many methods are used in the previous literature such as ANN, SVM, Naive Bayes classifiers and logistic regression. The original motivation of this work is to fill the gap between the very large dynamic data on educational institutions and the computational programming tools which is not sufficient to find solutions in some cases. The current work proposes a strategy based …
Electronic Learning Platforms And Their Impact On Education Quality At Faculties Of Tourism And Hospitality During Corona Pandemic, O. Jawabreh, R. Qaddhat, A. Jahmani, B. M. Al Najdawi, B. J. A. Ali, A. Ali
Electronic Learning Platforms And Their Impact On Education Quality At Faculties Of Tourism And Hospitality During Corona Pandemic, O. Jawabreh, R. Qaddhat, A. Jahmani, B. M. Al Najdawi, B. J. A. Ali, A. Ali
Applied Mathematics & Information Sciences
To effectively educate educations students, online platforms are crucial. Unfortunately, they might not be well- represented in universities. The goals of the study are determined in this light. The purpose of this paper is to analyze how the use of e-Learning has affected the quality of education in Jordans tourism and hospitality colleges during the recent Corona virus pandemic. Before doing regression analysis, a survey was sent out to faculty and employees at tourism and hospitality schools. Using SPSS version 22, researchers analyzed responses made on a 37-point Likert scale. An evaluation procedure was performed on it. The initial belief …
The Competitiveness Of Jordanian Tourism Activity In Enhancement Economic Growth, Mohammad H. Saleh, Omar Jawabreh, Emad Al Dein Al Fahmawee, Basel J. A. Ali
The Competitiveness Of Jordanian Tourism Activity In Enhancement Economic Growth, Mohammad H. Saleh, Omar Jawabreh, Emad Al Dein Al Fahmawee, Basel J. A. Ali
Applied Mathematics & Information Sciences
Competitiveness studies are regarded as one of the most essential at the worldwide level, particularly in the tourist sector, which is relying on to boost economic growth and living standards. The purpose of this study was to examine the competitive features of the Jordanian tourist industry, as well as the long-term equilibrium relationships between the factors of tourism activity and economic growth, using the Autoregressive distributed lag model (ARDL) over the period 1990- 2021. The study looked at the favorable benefits of tourism on employment, poverty reduction, and the Jordanian economys balance of payments. Using the koyck model, the study …
Application On The Validity Of Weak Compactness In Variable Exponent Spaces, A. A. H. Alrabiaa
Application On The Validity Of Weak Compactness In Variable Exponent Spaces, A. A. H. Alrabiaa
Applied Mathematics & Information Sciences
This research aimed to show the validity following Francisco L.Hern?ndez, César Ruiz and Mauro Sanchiz [1], of the necessary and sufficient conditions on subsets of variable exponent spaces 𝐿(·)(Ω) in order to be weakly compact. Useful criteria are given extending Andô results for Orlicz spaces. This research aimed to show that all separable variable exponent spaces are weakly Banach-Saks. Also, L-weakly compact and weakly compact inclusions between variable exponent spaces are studied.
Improving The Efficiency Of Median Filters Using Special Generated Windows, M. Abu-Faraj, A. Al-Hyari, B. Al-Ahmad, Z. Alqadi, B. J. A. Ali, K. Aldebe
Improving The Efficiency Of Median Filters Using Special Generated Windows, M. Abu-Faraj, A. Al-Hyari, B. Al-Ahmad, Z. Alqadi, B. J. A. Ali, K. Aldebe
Applied Mathematics & Information Sciences
Digital images of various types, gray and color, are used in many vital applications, necessitating the need to rid them of the noise that can infect them during the messaging process. One of the most important types of noise that negatively affects the characteristics of the digital image is salt and pepper noise, which leads to changing some of the pixels in the digital image to values of 0 or 255. The negative effect of this noise increases with the increase in the noise ratio (the number of affected pixels). This paper will discuss a new method to reduce the …
A Bounded Cumulative Hazard Model With A Change- Point According To A Threshold In A Covariate For Right-Censored Data, Fauzia Taweab, Noor Akma Ibrahim, Jayanthi Arasan
A Bounded Cumulative Hazard Model With A Change- Point According To A Threshold In A Covariate For Right-Censored Data, Fauzia Taweab, Noor Akma Ibrahim, Jayanthi Arasan
Applied Mathematics & Information Sciences
In most recent clinical studies, the focus is on estimation of the proportion of patients who are cured and who will therefore never experience the event of interest again. This article investigates a survival model with cure fraction and change-point effect based on the bounded cumulative hazard model (BCH). The maximum likelihood approach to estimate the unknown parameters is used. A major difficulty here is that the likelihood function is not differentiable with respect to a change point parameter. To address this problem a smoothed likelihood approach is proposed. Simulation studies have been conducted in this study to assess the …
Improving Aks Algorithm. Proving The Simplicity Of Integers, O. Kozachok
Improving Aks Algorithm. Proving The Simplicity Of Integers, O. Kozachok
Applied Mathematics & Information Sciences
Agrawal-Kayal-Saxena (AKS) theorem was proved, from which the above-mentioned algorithm is directly derived. The study has shown that the problem of simplicity is in the complexity class P of polynomial problems. An advanced AKS algorithm is proposed, which will simplify the initial AKS algorithm and ensure its implementation to determine the simplicity of integers. To implement this task it is necessary to reduce algorithm computational complexity. The block diagram of the algorithm for performing the advanced AKS test is presented. The theorems for prime numbers presented in the form of polynomials were formulated and proved. The AKS algorithm consisting of …
Numerical Solution Via A Singular Mixed Integral Equation In (2+1) Dimensional, A. R. Jan
Numerical Solution Via A Singular Mixed Integral Equation In (2+1) Dimensional, A. R. Jan
Applied Mathematics & Information Sciences
In this paper, under certain conditions, the unique solution of a mixed integral equation (MIE) with a singular kernel in position and a continuous kernel in time, in ( 2+1) dimensional is discussed and obtained in the space L2([a,b]×[c,d])×C[0,T],T < 1. After using a separation technique method, and Product Nystrom Method (PNM), we have a linear algebraic system (LAS) in two- dimensional with time coefficients. The convergence of the unique solution of the LAS is studied. In the end, and with the aid of Maple 18, many applications when a singular term of position kernel takes a logarithmic form and Carleman function are solved numerically. Moreover, the error is computed.
Anti-Phishing Tools: State Of The Art And Detection Efficiencies, M. F. Alghenaim, N. A. Abu Bakar, F. Abdul Rahim
Anti-Phishing Tools: State Of The Art And Detection Efficiencies, M. F. Alghenaim, N. A. Abu Bakar, F. Abdul Rahim
Applied Mathematics & Information Sciences
A phishing attack is a process of obtaining a customers private data, whether by using phishing emails or fake websites. With every new development on the Internet, the attackers means of phishing attacks develop, requiring more powerful phishing tools to counter these attacks. The Internet has become an essential part of the personal and social life of the public and governments, institutions, and companies all over the world. This means that Internet users need tools to protect against phishing attack types and web risks, which may cause personal, institutional, financial, and informational damage. Hence, this study reviews anti-phishing attack tools …
Building A Secure Image Cryptography System Using Parallel Processing And Complicated Dynamic Length Private Key, Mua’Ad Abu-Faraj, Abeer Al-Hyari, Bilal Al-Ahmad, Ziad Alqadi, Basel Ali, Abdullah Alhaj
Building A Secure Image Cryptography System Using Parallel Processing And Complicated Dynamic Length Private Key, Mua’Ad Abu-Faraj, Abeer Al-Hyari, Bilal Al-Ahmad, Ziad Alqadi, Basel Ali, Abdullah Alhaj
Applied Mathematics & Information Sciences
A method of color images cryptography will be introduced, programmed, and tested. The proposed method is based on using a digital color image as an image key; this image is to be kept secret without transmission. The proposed method will provide a high level of images protection based on the complicated and complex private key used in cryptography, this key will be changed when replacing the image key, or changing the data block size, or changing the color channel. The proposed method will be compared with other standard methods of data cryptography, and it will be shown how this method …
Modelling The South African Covid-19 Induced Web Traffic Data Shift Using Artificial Neural Networks, Judah Soobramoney, Retius Chifurira, Temesgen Zewotir
Modelling The South African Covid-19 Induced Web Traffic Data Shift Using Artificial Neural Networks, Judah Soobramoney, Retius Chifurira, Temesgen Zewotir
Applied Mathematics & Information Sciences
In response to the coronavirus pandemic of the year 2019 (Covid-19), several governments around the world restricted commercial, economic and socio-economic activities. For emerging markets like South Africa, the pandemic and subsequent restrictions have negatively impacted the financial standing of many sectors, corporates and households. Several corporates that rely on digital technologies such as website marketing experienced a steep decline in traffic flow onto the website and a distinct change in online behaviour. Whilst such change in online behaviour directly impacted the revenue of corporates, such data shifts posed further challenges to the accuracy of machine learning models that were …
Convergence Of Fuzzy Conformable Laplace Transform, Atimad Harir, Said Melliani, L.Saadia Chadli
Convergence Of Fuzzy Conformable Laplace Transform, Atimad Harir, Said Melliani, L.Saadia Chadli
Applied Mathematics & Information Sciences
The fuzzy conformable Laplace transform is defined in this study, and then some of its well-known features are studied. Furthermore, existence theorems for two convergences of the fuzzy conformable Laplace transforms are presented. As a result, as a new application of fuzzy Laplace transforms, we examine the solutions in state-space description of fuzzy linear continuous-time systems under generalized conformable differentiability.
Optimal Coordinated Search Problem For A Randomly Located Target, A. A. M. Teamah, A. A. Elbanna, H. A. Ismail
Optimal Coordinated Search Problem For A Randomly Located Target, A. A. M. Teamah, A. A. Elbanna, H. A. Ismail
Applied Mathematics & Information Sciences
The purpose of this paper is to study the coordinated search problem in which velocity of the searcher is a random variable. We are interested in finding a hole which randomly located on one of two disjoint oil pipelines or a cut in one of two lines of the power cable under sea surface. There are two searchers on every line that start the searching process from the origin of their line. In addition to calculating the expected value of the detection time, we derived the conditions which can minimize this expected value.:
Decision Support Approach Based Rough Sets Theory To Investigate The Relationship Between Personality Traits And Drug User (Year-Based Definition), Abdelbaset A. Hares, H. A. Mohamed, Miad Abu Hawsah
Decision Support Approach Based Rough Sets Theory To Investigate The Relationship Between Personality Traits And Drug User (Year-Based Definition), Abdelbaset A. Hares, H. A. Mohamed, Miad Abu Hawsah
Applied Mathematics & Information Sciences
There is no doubt that the use of drugs has significant consequences for society, it introduces risk into the human life, increasing risk of poor health and greater earlier mortality and morbidity. The rapid growth of artificial intelligence and machine learning can provide useful tools for analyzing this problem; various methods have been given by researchers for increasing the prediction rate of drug users. This work proposes a decision support approach to investigate the relationship between drug user (year-based user definition) and personality traits. Psychologists approved the recent personality traits Five Factor Model (FFM) for understanding human individual differences. Two …
Artificial Intelligence Security Model For Privacy Renitence In Big Data Analytics, S. Saravanan, M. Sivabalakrishnan, N. Duraimurugan, D. Divya
Artificial Intelligence Security Model For Privacy Renitence In Big Data Analytics, S. Saravanan, M. Sivabalakrishnan, N. Duraimurugan, D. Divya
Applied Mathematics & Information Sciences
The smart city uses Information and Communication Technologies (ICT) to build, run and sustain the environment, economic methods to overcome the growing problems of urbanization. Security, security, secrecy and validity have all been important factors in smart city applications, and they are also important in smart city infrastructure interfaces.Hence In this research, an Artificial Intelligence-Big Data Model (AIBM) was developed to enhance the data protection elements of information management interfaces in different smart city applications to address these concerns. A divergent evolutionary method has been implemented in AIBM to provide adequate security for the Secret Data Domain Controller for smart …
A Multi-Index Generalized Derivative; Some Introductory Notes, M. Vivas-Cortez, L. M. Lugo, Juan E. Na ́Poles Valde ́S, M. E. Samei
A Multi-Index Generalized Derivative; Some Introductory Notes, M. Vivas-Cortez, L. M. Lugo, Juan E. Na ́Poles Valde ́S, M. E. Samei
Applied Mathematics & Information Sciences
In this work we present a generalized multi-index derivative, which contains as particular cases, with an index, several local derivatives known from the literature (both conformable and non-conformable). Obviously this new development contains many of the desirable properties of integer derivatives. It is worth noting that the multi-index differential operator departs from the classic single-order local derivatives, as in the case of the particular cases presented, which leads to an adequate and useful mathematical tool to generalize widely accepted results, with applications potentials to Physics, fundamental within mathematical simulation.
Best Proximity Point Of Generalized (F − Τ )-Proximal Non-Self Contractions In Generalized Metric Spaces, Abdelkarim Kari, Hasanen A. Hammad, Adil Baiz, Mouline Jamal
Best Proximity Point Of Generalized (F − Τ )-Proximal Non-Self Contractions In Generalized Metric Spaces, Abdelkarim Kari, Hasanen A. Hammad, Adil Baiz, Mouline Jamal
Applied Mathematics & Information Sciences
In this manuscript, we introduce the idea of generalized (F,τ)-proximal contraction and prove new best proximity results for these contractions in the context of a generalized metric space. Our findings extend and generalize a number of previous results from the literature. Also, We present an example to illustrate the applicability of our results. Keywords:
Convergence Of Fuzzy Conformable Laplace Transform, Atimad Harir, Said Melliani, L.Saadia Chadli
Convergence Of Fuzzy Conformable Laplace Transform, Atimad Harir, Said Melliani, L.Saadia Chadli
Applied Mathematics & Information Sciences
The fuzzy conformable Laplace transform is defined in this study, and then some of its well-known features are studied. Furthermore, existence theorems for two convergences of the fuzzy conformable Laplace transforms are presented. As a result, as a new application of fuzzy Laplace transforms, we examine the solutions in state-space description of fuzzy linear continuous-time systems under generalized conformable differentiability.
A Multi-Index Generalized Derivative; Some Introductory Notes, M. Vivas-Cortez, L. M. Lugo, Juan E. Na ́Poles Valde ́S, M. E. Samei
A Multi-Index Generalized Derivative; Some Introductory Notes, M. Vivas-Cortez, L. M. Lugo, Juan E. Na ́Poles Valde ́S, M. E. Samei
Applied Mathematics & Information Sciences
In this work we present a generalized multi-index derivative, which contains as particular cases, with an index, several local derivatives known from the literature (both conformable and non-conformable). Obviously this new development contains many of the desirable properties of integer derivatives. It is worth noting that the multi-index differential operator departs from the classic single-order local derivatives, as in the case of the particular cases presented, which leads to an adequate and useful mathematical tool to generalize widely accepted results, with applications potentials to Physics, fundamental within mathematical simulation.
Optimal Coordinated Search Problem For A Randomly Located Target, A. A. M. Teamah, A. A. Elbanna, H. A. Ismail
Optimal Coordinated Search Problem For A Randomly Located Target, A. A. M. Teamah, A. A. Elbanna, H. A. Ismail
Applied Mathematics & Information Sciences
The purpose of this paper is to study the coordinated search problem in which velocity of the searcher is a random variable. We are interested in finding a hole which randomly located on one of two disjoint oil pipelines or a cut in one of two lines of the power cable under sea surface. There are two searchers on every line that start the searching process from the origin of their line. In addition to calculating the expected value of the detection time, we derived the conditions which can minimize this expected value.:
Optimization Task Scheduling Bee Colony Algorithm For Heterogeneous Cloud Computing Systems, Ahmed Y. Hamed, M. Kh. Elnahary, Hamdy H. El-Sayed
Optimization Task Scheduling Bee Colony Algorithm For Heterogeneous Cloud Computing Systems, Ahmed Y. Hamed, M. Kh. Elnahary, Hamdy H. El-Sayed
Applied Mathematics & Information Sciences
The primary purpose of the task scheduler is to assign tasks to available processors to produce a minimum Makespan without violating precedence constraints. In heterogeneous cloud computing resources, task assignments and schedules significantly impact system operation. In the experimental task scheduling algorithm, a different mapping of the process will result in a different maximum completion time of a batch of tasks (Makespan) on heterogeneous cloud computing resources. Thus, a scheduling algorithm has to define a schedule considering the precedence of child tasks depending on the resources required to reduce makespan. In this paper, we propose an Efficient Artificial Bee Colony …
Decision Support Approach Based Rough Sets Theory To Investigate The Relationship Between Personality Traits And Drug User (Year-Based Definition), Abdelbaset A. Hares, H. A. Mohamed, Miad Abu Hawsah
Decision Support Approach Based Rough Sets Theory To Investigate The Relationship Between Personality Traits And Drug User (Year-Based Definition), Abdelbaset A. Hares, H. A. Mohamed, Miad Abu Hawsah
Applied Mathematics & Information Sciences
There is no doubt that the use of drugs has significant consequences for society, it introduces risk into the human life, increasing risk of poor health and greater earlier mortality and morbidity. The rapid growth of artificial intelligence and machine learning can provide useful tools for analyzing this problem; various methods have been given by researchers for increasing the prediction rate of drug users. This work proposes a decision support approach to investigate the relationship between drug user (year-based user definition) and personality traits. Psychologists approved the recent personality traits Five Factor Model (FFM) for understanding human individual differences. Two …
Artificial Intelligence Security Model For Privacy Renitence In Big Data Analytics, S. Saravanan, M. Sivabalakrishnan, N. Duraimurugan, D. Divya
Artificial Intelligence Security Model For Privacy Renitence In Big Data Analytics, S. Saravanan, M. Sivabalakrishnan, N. Duraimurugan, D. Divya
Applied Mathematics & Information Sciences
The smart city uses Information and Communication Technologies (ICT) to build, run and sustain the environment, economic methods to overcome the growing problems of urbanization. Security, security, secrecy and validity have all been important factors in smart city applications, and they are also important in smart city infrastructure interfaces.Hence In this research, an Artificial Intelligence-Big Data Model (AIBM) was developed to enhance the data protection elements of information management interfaces in different smart city applications to address these concerns. A divergent evolutionary method has been implemented in AIBM to provide adequate security for the Secret Data Domain Controller for smart …
Peristaltic Flow For A Mixture Of Blood And Gas Bubbles In The Vertical Inferior Mesenteric Vein, A. A. Elbendary, S. A. Mohammadein, F. A. El Hussiny, S. M. Elkholy, M. S. Ali
Peristaltic Flow For A Mixture Of Blood And Gas Bubbles In The Vertical Inferior Mesenteric Vein, A. A. Elbendary, S. A. Mohammadein, F. A. El Hussiny, S. M. Elkholy, M. S. Ali
Applied Mathematics & Information Sciences
In this paper, the viscous blood concentration and gas bubbles flow in the peristaltic vertical inferior mesenteric vein (IMV) are studied. The mass, concentration, and Navier-Stokes equations introduce the mathematical simulation of the current problem in the case of long wavelength and low Reynolds number with an analytical solution. The results introduced that the gradient pressure of a mixture of blood flow with gas bubbles performs larger values than that of blood without gas bubbles. Moreover, the blood concentration, velocity of blood and gas bubbles are very sensitive to the small change in blood density ratio, amplitude ratio, and modified …