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Sixth International Scientific Conference for Iraqi Al Khwarizmi Society (FISCAS) 2020 was held in 22-23 November 2020, Cairo, Egypt during. Sixth International Scientific Conference of Al-Khwarizmi Society is organized by Al-Iraqa Organization for Training and Conferences (Represented by M.R Hayder Al-Shanan. The conference provides a useful and wide platform both for display the latest research and for exchange of research results and thoughts in Physics and Mathematics and other disciplines related to Statics and Technology. The participants of the conference were from almost every part of the Iraqi Universities, with background of either academia or research. The success and prosperity of the conference is reflected high level of the papers received.

The proceedings are a compilation of the accepted papers and represent an interesting outcome of the conference. This conference totally includes 85 papers and covers 5 main field of research: 1. Mathematics; 2. Physics; 3. Computer Vision; 4- Algebra and 4. Statistics.

List of SCIENTIFIC COMMITTEE is available in this pdf.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

Type of peer review: The papers in the conference were all Triple-blind review.

● Conference submission management system: OJS

● Number of submissions received: 150

● Number of submissions sent for review: 125

● Number of submissions accepted: 84

● Acceptance Rate (Number of Submissions Accepted/Number of Submissions Received X 100): 56%

● Average number of reviews per paper: 2

● Total number of reviewers involved: 3

● Any additional info on review process:

● Contact person for queries:

Prof. Dr. Noori Farhan Al-Mayahi Al-Khwarizmi Society Chair Contact Info: Institute: college of scientific/university of Al-Qadisiya/mathematics department. E-mail: nfam60@yahoo.com. ● Mobile: 009647801432941

It is well-known that grey system theory was put forward in the statistical literature to overcome the problem of partially unknown parameters, therefore it is given the attention of the researchers in many scientific areas. Therefore, many methods have been presented in which the grey system is combined with the Fourier series and others for more accurate prediction. This paper presents a methodology to modify the method of least squares based on Fourier series residuals that are computed by using grey system theory. The objective of this methodology is to improve the estimates of a modified exponential growth model. The performance of the proposed method by using simulation is compared with two famous methods and the results show our proposed method outperforms more than others and it is highly efficient and reliable. On the practical, the new method was used to predict the price of a barrel of crude oil for the OPEC basket for the period from Jul 2019 to Dec 2019, and It can be seen that OPEC basket prices will decline in the end of 2019.

In Current research, the study suggested that distribution is using for the exponential quantile function to define the W distribution. Correspondingly, there are many general properties of T-X system of distributions are considered. As a result, this study was obtained a new aspect of distribution by deriving the T-X family equation. After that the study was covered different mathematical and statistical properties, as well as the moments Reliabilities Analysis,) failure, reverse hazard) rate of the distribution derived. The parameters were valued by the maximum likelihood method.

The adoption of eLearning in developing countries is rare when a comparison is made against the developed nations. Therefore, this study answered calls from numerous literature demanding for more research to investigate the adoption, usage, and application of eLearning systems and applications in Libyan higher education institutions (LHEIs) to contribute to this crucial knowledge gap. Thus, a systematic literature review (SLR) was conducted focusing on the eLearning technology acceptance theories and models and open issues and challenges facing the LHEIs. Hence, the findings revealed that the technology acceptance model (TAM) is the most dominant theoretical model applied to test the adoption of eLearning in LHEIs. The finding further revealed that there are limited studies based on other technology acceptance theories such as the unified theory of acceptance and use of technology (UTAUT), the theory of reasoned action (TRA), and the theory of planned behavior (TPB). Hence, this study recommends the adoption of the UTAUT framework for future research due to its foundation from eight different technology acceptance models, including the dominant TAM theory, which could offer new insights. The findings of this study have the potential for academic researchers wanting to study the acceptance and use of technology for teaching and learning especially in developing countries.

Data clustering determines a group of patterns in a dataset which are homogeneous in nature. The objective is to develop an automatic algorithm which can accurately classify an unleveled dataset into groups. The K-means method is the most fundamental partitioned clustering concept. However, the performance of K-means method is fully depending on determining the number of clusters, K, and determining the optimal centroid for performing the clustering process. In this paper, an adaptive firefly optimization algorithm, which is a nature-inspired algorithm, is employed to improve the K-means clustering. The experimental results of clustering two real datasets show that the proposed method is able to effectively outperform other alternatives methods.

The paper deals with the comparison between the methods of estimating the reliability of arriving at the time of the trip for the Burr distribution, namely (Maximum likelihood method, the Bayes method, the non-linear least squares method). We are comparing among the three estimation methods using the simulation method. To make an understanding of the best method for estimating the reliability of arriving at the Burr distribution through a comparison between the three methods, an integrative mean square error standard (IMSE) was used, as the simulation results showed the preference of the Bayes method over the other methods.

Image denoising is process of removing the noise (i.e. artifacts) in digital image. Noise reduction is an essential process of image processing in order to improve, analyze and interpret important information in an image. Edges are important to the visual appearance of images, to preserve important features such as edges and corners during the noise reduction process. A class of fourth- and second-order partial differential equations (PDEs) are used to optimize the trade-off between noise removal and edge preservation. Image quality assessment plays an important role in various image processing applications. It is still an active field of research. Several techniques have been suggested for measuring image quality but none of them are ideal for measuring the quality. This paper presents a new assessment of image quality based on topological data analysis (TDA) which is used for evaluating noise removal from colour images and also for assessing the performance of PDE-based denoising models. The experimental results show that the proposed assessment model gives high correlation. Furthermore, the proposed method provides very low computational load and similar extraction of characteristics to human perceptional assessment.

In this paper, we have been used Bayes Technique depending on the normal conjugate function to estimate parameters of the multiple regression model, and we have been tested significance of this model. The test showed in the application that the mean square error (MSE) for the used model was decreasing, also it showed that the determinant coefficient is increasing highly. In the same time, value of the computed F-test was significant according to the above we can consider that the model is significant

The estimators of Gumbel type-II distribution parameter was set by using Maximum likelihood method (MLE) and Bayesian method, under many types of Loss functions; Linex Loss Function (LLF) Modified Linex Loss Function (MLLF), Balanced Linex Loss Function (BLLF), and Compound Linex Loss Function (CLLF) using Gamma prior.

One of the ways to compare the different estimators, and find the best method for estimation which used in this paper, Mean Squared Error (MSE) and Root Mean Square Error (RMSE), was used based on a Monte Carlo Simulation (MCS).

Finally, the discussion and illustrate of comparison results was showed and summarized in tables.

Quality control is one of the effective statistical tools in the field of productivity control to monitor and match manufactured products to standard specifications and approved standards for some goods and services, and their purpose is to keep pace with the production and industrial development in the labour market and competition. Naturalness in the productive process. The SVM method was used (Support Vector Machine) It is one of the algorithms that are used to solve classification problems or determine the limits of control in monitoring the production process in the fact that the data do not follow the normal distribution or have an unknown distribution, as the research aims to monitor the production process through several variables at the same time to reflect the quality The material produced. The drinking water test data for the old Shatra water project was used to clarify the method of operation of the backing wave machine method, as the standard drawing method was adopted to indicate the performance and efficiency of the method used, and its performance was good to know the quality of the.

In the context of kernel nonparametric regression, the curve estimation is fully depending on the smoothing parameter. At this point, the nature-inspired algorithms can be used as an alternative tool to find the optimal selection. In this paper, a bat optimization algorithm method is proposed to choose the smoothing parameter in Nadaraya-Watson kernel nonparametric regression. The proposed method will efficiently help to find the best smoothing parameter with a high prediction. The proposed method is compared with four famous ` of prediction capability.

In this paper, a new hybrid algorithm for linear programming model based on Aggregate production planning problems is proposed. The new hybrid algorithm of a simulated annealing (SA) and particle swarm optimization (PSO) algorithms. PSO algorithm employed for a good balance between exploration and exploitation in SA in order to be effective and efficient (speed and quality) for solving linear programming model. Finding results show that the proposed approach is achieving within a reasonable computational time comparing with PSO and SA algorithms.

Semiparametric regression models are extensions of linear regression models to include a nonparametric function of some explanatory variables. In semiparametric regression model researchers often encounter the problem of multicollinearity. In the context of ridge estimator, the estimation of shrinkage parameter plays an important role in analyzing data. In this paper, numerous selection methods of the shrinkage parameter of ridge estimator are explored and investigated. Our Monte Carlo simulation results suggest that some estimators can bring significant improvement relative to others, in terms of mean squared error.

Recently, machine learning methods such as regression trees, Support Vector Machine and lasso have been widely used in many scientific fields where the variance of the random errors is homogenous or constant. This issue is disagreement with the data that is based on the time, such as financial data which is analysis by using time series. Unfortunately, the financial time series is instable as a result of fluctuations that happen during different time periods between relative calm and high turbulence. A great effort was paid in the literature to tackle this problem by combining machine learning with GARCH model. In this paper, we suggest estimating the variance of varying-time and parameters of machine learning methods to predict the exchange rate of the Iraqi dinar (IQD) against (USD) with using an iterative procedure. Real data and simulation study are curried out to know the performance of our proposed procedure with others. The result shows that our proposed procedure outperforms than others.

This paper deals with some Estimator of Bayes s of the parameters of Gamma distribution (GD) under three different loss functions, represented via Precautionary loss function, Entropy loss function (ELF) and invariant of scale squared error (SE) loss function, assuming Gamma and Exponential priors for the shape and scale parameters respectively. Maximum likelihood estimator (MLE) and Lindley's approximation are used to obtain the Bayes estimates of the shape and scale parameters of GD. According to the Monte Carlo simulation method, those estimators have been compared based on the mean SEs (MSE's). The results show that the performance of the Estimator of Bayes s under invariant of scale SE loss function produces the best estimates for the two parameters in all cases.

Gumbel probability distribution is an important probability distribution that has wide applications in various fields such as engineering, physics, hydrology, geology, etc. The study aims to generate a new truncated distribution by truncate the probability density function of the first type Gumbel distribution from the left side to obtain the Truncated Gumbel distribution from the left side within the period (0, ∞). As we work in this paper on the derivation of the new truncated distribution formula and its characteristics. As well as discussing different methods of estimating its parameters, represented by the maximum likelihood method and Percentiles Estimation Method, then making a simulation of the comparison between methods of estimation.

One of the powerful and a promising model which is used to understand the structural relationship between the chemical activity and the chemical compounds is the quantitative structure-activity relationship (QSAR). However, the huge in dimensionality is one of the major problems which affect the quality of the QSAR modeling. Penalized methods are an attractive framework that have been adapted and gained popularity among researchers as the key for performing descriptor selection and QSAR model estimation simultaneously. The choice of the tuning parameter of the penalized methods is critical. Our aim of this paper is to efficiently estimate such a tuning parameter by using bat algorithm (BA), which is a king of nature-inspired algorithms. Experimental results, obtained by running on two datasets, show that our proposed method performs better than other methods, in terms of prediction, number of selected descriptors, and running time. Further, the Y-randomization test and applicability domain confirm that the constructed QSAR model by BA method is reliable and robust.

In this article, we present that fractional Lévy processes which is very an important field in both probability theory and its application in recent years. The fractional Brownian motion is suggested as the fractional Lévy processes in this article. We will make parameters estimate of the Vasicek process driven by fractional Brownian motion, that represented the short memory parameter (0 < H < ½) and the long memory parameter (½ < H < 1). So, Our aim is to study the behavior of stochastitc Vasicek Interest driven by fractional Brownian motion. We use maximum likelihood to estimate the drift, diffusion and Hurst parameters and generally the fractional Lévy processes. We illustrate our methods, and show the behavior of stochastic parameters using simulation and real data (ISX60).

In this article, we proposed a model-free variable selection method (SMAVE-EN). The concepts of sufficient dimension reduction (SDR) and regularization methods are combined to introduce SMAVE-EN. This method is proposed to produce a shrinkage estimation when the predictors are highly correlated under SDR settings. The advantage of SMAVE-EN is that SMAVE-EN extended Elastic net (EN) to nonlinear and multi-dimensional regression under SDR settings. From another side, the SMAVE-EN enables MAVE to work with problems were the predictors are highly correlated. In addition, SMAVE-EN can exhaustively estimate dimensions, while selecting informative covariates simultaneously under SDR framework. The effectiveness of SMAVE-EN is evaluated by both simulation and real data analysis.

The ridge estimator has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The negative binomial regression model (NBRM) is a well-known model in application when the response variable is a count data with overdispersion. However, it is known that the variance of maximum likelihood estimator (MLE) of the NBRM coefficients can negatively affected in the presence of multicollinearity. In this paper, the generalized ridge estimator is proposed to overcome the limitation of ridge estimator. Several methods for estimating the shrinkage matrix have been adapted. Our Monte Carlo simulation results suggest that the proposed estimator, regardless the type of estimating method of shrinkage matrix is better than the MLE estimator and ridge estimator, in terms of MSE. In addition, some estimating method of shrinkage matrix can bring significant improvement relative to others.

In this paper, a new survival model is being defined. This model is adaptable for produce a new lifetime distribution for analyzing positive data. We define a new lifetime models called the Transmuted-Survival-Exponential distribution (TSE). Essential functions associated with the proposed distribution are obtained. Some structural properties of the new models are investigated. The new formula may serve as a flexible transmuted to other distributions for modeling survival data arising in several fields of science such as hydrology, biostatistics, metrology and engineering

The occurrence of tremendous developments in the field of data has led to the formation of huge volumes of data, and it is natural that this leads to the presence of outliers in this data for many reasons. The presence of outliers in the data affects the statistical analysis, so we must try to reduce their impact in various ways. On the other hand, the existence of outliers may be of great benefit in many application and of great importance in various fields. In this paper we propose a new method for detecting outliers based on the Particle Swarm Optimization algorithm (PSO). The new propose algorithm was compared with the normal distribution method, and the results obtained from the new method were very promising and encouraging.

Speedy increase in the employ of the content of multimedia is very commonly perceived in existing generations. Video is one of the extreme exceedingly recovered data of multimedia which can provide quick fixes and immediate gratification for whole the kinds of user information willingness. Detection of Key frame from Videos and classification of videos are the necessary protocols in the complements tasks of video retrieval. The aim of this research is to compare between histogram similarity and histogram differencing for more brief key frames extraction from video stream. The suggested system for key frame extraction has three steps. Firstly, the video frames series will take and the characteristics for points of interest are elicited utilizing SUSAN detector. After eliciting interest characteristics from all video frames images, secondly, K-Means clustering technique was utilized for these features to construct the clusters with a number of interest points. Thirdly, a histogram builds for each video frame based on numbers of features in each cluster. X-axis of a histogram represents the cluster number and y-axis represents the number of features in each cluster. For key frames extraction, numbers for each cluster can be offered and a query histogram can be constructed based on entered clusters' numbers. A query histogram was matched with every video frame histogram using Manhattan distance to discover the similar histogram to query histogram. After chosen similar histogram, it can extract all key frames from that video frames. The experimental results show that the number of key frames extracted from the video is very brief when using the histogram similarity compared to the histogram differencing. For example, the number of key frames extracted from a car video is 70 when using the histogram similarity, while it is 180 when using the histogram differencing.

In this paper, we described a new method for moving objects (detection and tracking). The first step to determine the object tracking is the segmentation process through getting a background image and then comparing it with the foreground image. Separation of the background image from the foreground image is the result of this step to obtain an object. In further step, enhance the segmentation operation by using morphology to remove small noise. Finally, select the largest object, center and radius of the largest. Therefore, we can detect the object perfectly and then the tracking of all objects. In this process for finding out the location of the target, we observed less error in detection and was very accurate.

Due to the huge expand in global markets and financial transactions, the importance of E-commerce has grown significantly, so to achieve fully functioning, scalable, reliable, efficient, secure, and user-friendly E-commerce system, Adequate system analysis and design procedures are essential. On the other hand The internet vast growing has totally altered the way most companies work. The Internet has created a means for e-Commerce the internet has created a way to provide a unique avenue for companies and customers to sell and buy goods and services. When creating an e-commerce website, there are several goals that must be taken into account, one of them is how to Increase the site's efficiency to ensure customer turnout and thus achieve the required material profits. There are several methods that are followed to increase the efficiency of the site. One of these methods is the recommender system. This paper produces a study overview of the value of recommended systems and thoroughly analyzed Collaborative Recommender System (CF) techniques with its techniques., which presents proposals to customers according to their interests, making it easier for the customer to search and thus choose the goods that suit him.

Datum embedding or information hiding is a method that accepted us to secret embedded and extracted data from any file, such as picture file, a video file, and sound file. The base algorithm in steganography is the embedded and extraction algorithms. The objective of this paper is hiding a secret message in video frame to prevent an attacker from accessing the message.

This paper suggested new algorithm to hide secret message in video, after convert video to number of frames, it takes each video frame applied the power low transform (PLT) in 3 or 3.5 or 4. In this paper takes power low transform only 3.5 to hide secret message in each video frame uses the secret key, the secret key is curve of cosh-exponential, each point in curve selected the location in frame to hide one bit from frame video. It obtains stego-frame video to Transmitted the for IoTs, and save in database in IoTs, and any authors can be access to this stego-frame video in database to known secret key. The outcome of this algorithm is very good in steganography video, it uses power low transform to obtain the high security, transparency, high capacity in secret message and powerful. These results are obtaining many tests PSNR, MSE, Entropy, Correlation coefficient, Histogram, and Capacity.

In recent few years, deep learning has fast growing in many fields as natural language processing, image recognition, handwriting recognition, computer vision, and speech recognition. Automatic speech recognition (ASR) is a technique that refers to translating spoken words from an acoustic waveform into a text equivalent to what the speaker says. More recently, the advances in deep learning can support ASR in improving the performance of systems accuracies. Arabic is a Semitic language, one of the oldest used and most communicated languages in the world. But, it least concentrated in the case of Arabic speech recognition and under-resourced languages. This paper presents a survey that focuses on an automatic speech recognition system based on isolating words technique for Arabic speech. It also highlights the facilities and tools for developing speech recognition systems. This work is intended to be a useful starting point for those who are interested in ASR.

Artificial Intelligence Techniques, and image processing are playing a major role in medical science. In this paper, several methods of artificial intelligence techniques were used to diagnose Gingivitis disease. The Bat swarm algorithm, the Self-Organizing Map(SOM) algorithm and the Fuzzy Self-Organizing Map (FSOM)network algorithm were used to diagnose Gingivitis disease. Also, was used the traditional algorithm, which is the Principal Component Analysis (PCA) algorithm, for Feature Extraction of Gingivitis disease images. We compute the diagnostic accuracy on this images dataset. Next, we compared the final results of these three methods used and applied to this data. In this paper the best of these methods is the BAT, because in testing state the BAT was obtained higher accuracy for diagnose of Gingivitis disease equal (97.942%).

Digitization and technological transformation in providing various services have become a goal for many countries in light of the current digital revolution to implement the concept of a smart city. Given the great importance of the smart city concept by researchers, the overriding concern is how to maintain data security and user privacy. These two criteria can or directly represent the strengths and weaknesses of such technology projects. This paper included a comprehensive study of the smart city, its concept and components. The research also included a detailed study of the most important applications included in smart city services and their working mechanisms and uses. The diversity of applications and services provided under the smart city environment is proof of the importance of this model. The paper also reviewed the security risks of data in all stages of work, data collection, data transfer and processing. Finally, the paper reviewed the five most important technologies used in a smart city to maintain information security and data privacy, their advantages, their internal methodology and algorithms. In the end, this paper aims to give a clear picture of all the details of the smart city and the technologies used for the purpose of ensuring information security and data privacy.

Software project cost prediction is a very important task during building and developing software projects. This process helps software project engineers to accurately manage and plan their resources in terms of cost estimation. However, Need for accurate cost development prediction model for a software project is not a simple procedure. Predicting the cost required while developing software engineering projects is the most difficult challenge that attracts the attention of researchers and practitioners. This paper adopts a new model in estimating the cost of building or developing software engineering projects using a machine learning approach. The results proves that machine learning methods can be used to predict program cost with high accuracy rate compared with traditional software estimation techniques. The proposed model in this research was trained on the NASA (National Aeronautics and Space Administration) data set, which contains the characteristics of 60 projects in addition to the real cost of the projects. An analysis of the results of the implementation for the proposed methods showed that the cost Predicting process using K-Nearest Neighbours algorithm (KNN), Cascade Neural Networks (CNN) and Elman Neural Networks (ENN) It has the ability to predict the costs required to build or develop software engineering projects, K-Nearest Neighbours algorithm has shown high accuracy for Predict the required cost to develop Software Engineering projects Compared to Cascade Neural Networks and Elman Neural Networks ENN.

In this work, a combined technique the Variation Iteration Method (VIM) with the Trapezoidal Rule (TR) was recommend to solve linear and nonlinear fractional ordinary differential equations (F.O.D.E.), where the results obtained from the Variation Iteration method were improved, and numerical results were obtained by determining the maximum absolute errors (MAE) and mean square error (MSE) for the given examples. As the results It is proved that that the proposed method is better than the default method.

The main objective of this paper is define the notion Nano-αg_Ị-open set by using nano topological space and some properties of this set are studied also, nano-αg_Ị-β set and nano-αg_Ị-θ-closed set are two concepts that are defied by using Nano-αg_Ị-open set many examples have been cited two indicate that the reverse of the proposition and remarks is not true. Also an applied example was presented explains how to benefit from nano-αg_Ị- set.

The aim of this work is to study new sets of soft closed and soft open sets by using soft pre-open sets with collection of a soft ideal which is said to be an a soft-ᶅ-pre-g-closed and soft-ᶅ- pre-g-open sets with some properties, examples and relationships between these concepts with soft pre-g * - closed and soft pre-g *-open.

New concepts of soft open and soft closed functions are defined by using these sets with some examples and scheme. Also, many continuous function by using these with examples and schemes are explained.

In the current paper, the coupled of space -time fractional of both the equal width wave equation(FCEWE) and the modified equal width wave equation (FCMEWE) are formally solved. For this purpose, the conformable derivative and Sine-Cosine method have been introduced to reduce these equations into the ordinary differential equations then the exact solution was extracted. The search results showed the possibility of using this method successfully for solving the FCEW and FCMEW equations at different time levels.

We proposed and analyzed a predator–prey model. The disease effects in predator due to pollution in environment, as well the immigration factor effected is discussed. We assumed that, the population are divided into three parts prey, susceptible predator and infected predator. Firstly, the existence, uniqueness and bounded-ness of the solution of the model are discussed. Secondly, we studied the existence and local stability of all equilibrium points. Furthermore, some of the Sufficient conditions of the global stability of the positive equilibrium are established using suitable Lyapunov functions. Finally, those theoretical results are demonstrated with numerical simulations.

In this paper, we establish random fixed point theorems for random contractive condition of integral type in complete metric space under RX–contraction. Also we prove common random fixed point theorems using random operator satisfying random conditions of integral type and RX.

Clustering is the main procedure for data mining with a wide application such as gene analysis. Clustering is a method of separates (grouping) previously unclassified data on the basis of its features, and it is an unsupervised learning problem that divides that data into groups in such a way that it makes those data in the same group more similar to each other compared to in other groups. Penalized regression-based clustering is an extension of the "Sum Of Norms" clustering model. In this paper, the nature-inspired algorithm is employed to improve the penalized regression-based clustering to better estimation. The real data application on gene expression data results suggests that our proposed improvement can bring significant improvement relative to others.

In the present work, we introduce the notion of pseudo-seminorm, then we established, a criterion for the metrizability of a pseudo vector space 𝛯 with a pseudo topology 𝜏. It is specified, that for the metrizability of 𝛯 is necessary and sufficient that 𝛯 is first countable. Moreover, a sufficient condition for existence a base for the filter of neighborhoods of zero is proved and demonstrated that this condition introduces a compatible pseudo topology with the algebraic vector space structures.

The aim of this research is to study the modern sort of open sets that is said -g-closed. Some functions by this notion was explained and the relationships among them like continuous function g-continuous function strongly- g-continuous function and g-irresolute function.

The purpose of the present paper is to evaluate the error of the approximation of the function F defined in [0,1] by Bernstein polynomial in L_P space (0 < P ≤ 1).

We study the direct relation between the degrees of approximation of Riemann integrable functions with respect to algebraic polynomials with average modulus of smoothness ${\tau }_{2}(f,{\rm{\Delta }}\frac{1}{\sqrt{j}})$ the locally global spaces (L_δ,P), (0 < P ≤ 1) wich is importance for the approximations theory.

The goal of this research is to study the nonlinear second order delay eigenvalue problems which consists of delay ordinary differential equations, in fact one of the expansion methods that is called the Collocation method will be developed to solve this kind of problems.

Peristaltic transport and heat and mass transfer on a power-law fluid flow in an elastic tapered tube with variable cross-section induced by dilating peristaltic wave was illustrated in this paper. Problem was studied under the assumption of long wavelength (δ ≪ 1) and low Reynolds number (Re ≪ 1). The different emerging parameters effect are explained graphically for the exact solutions of the temperature distribution, heat transfer coefficient, rate of heat transfer and concentration of particles. The results showed that the temperature distribution and heat transfer coefficient are an increasing functions of the parameters power-law index n, dilation parameter k, amplitude ratio ϕ and volume of flow rate F whereas they are decreasing functions when the non-uniform parameter b increases. It is noted an opposite behaviour for the rate of heat transfer and concentration distribution. MATHEMATICA software is used to plot all figures.

The goal of the article is to extend and study the proper fixed spaces. The sets called D-, and Kernel sets in this space have been studied and introduced. In this paper we include theorems and examples related to these concepts in fixed topological space. This research finds the characteristics and properties of such notions. Also the relation between them are studied and investigated in fixed topological spaces. Since the definition of the mathematics usual topology differs from the definition of fixed topology, we have noticed that some of the concepts that have been studied in both are different in terms of their verification in the proofs and examples and evidence for that the of definitions D-sets. α, R₀, D₀, D₁ - spaces and the kernel set. Also we were obtained that the relationships between these concepts are different from those in previous studies.

By using the theory of residues of holomorphic functions, one formula is obtained for the product of a finite number of Sines of multiple arcs and one improper integral is computed.

In this study, the concept of infinite quasi-Sobolev spaces ${ {\mathcal L} }_{{\rm{\infty }}}^{m}$, where m ∈ is considered. These spaces have been proved as quasi-Banach spaces, as well as, Banach spaces, while they neither Hilbert spaces nor quasi-Hilbert spaces. Some kinds of linear operators such as continuous, bounded, closed and completely continuous for operators which map ${ {\mathcal L} }_{{\rm{\infty }}}^{m}$ or ${ {\mathcal L} }_{1}^{m}$ into ${ {\mathcal L} }_{{\rm{\infty }}}^{m}$ are discussed.

In this work, the alternative version of the ElGamal public key cryptosystem (EPKC) first is proposed. The revised EPKC depended on an extended discrete logarithm problem over matrices. More secure communications with the revised EPKC in compare to the original one are obtained. Also, a new public key cryptosystem has been designed based on undirected complete graph (UCG). The plaintext data is selected as a subset from the finite fields which is corresponded to undirected complete graph G(V,E), where V and E are finite sets of the vertices and edges respectively. The plaintext is encrypted using the matrix power function (MPF) and the minimum spanning tree (MST) problem of undirected complete graph (UCG). The adjacent matrix representation of MST is used to speed up the calculations. More secure on the proposed cryptosystem has been determined in compare to other asymmetric public key cryptosystems. New computational results of the revised EPKC and the UCG-based public key cryptosystem are discussed.

Several mathematical concepts from analytics number theory, especially the counting functions (CFs) are employed to solve some modern problems in mathematics, computer sciences, engineering and others. One of them is the factorization problem for integers into two primes. This work proposes an extended factorization problem using the CFs, as main part from analytics number theory, to factor a real number r into two primes p and q. The computations of the points doubling and addition on the elliptic curves E modulo a composite number n are also used in this extension to give new two versions of the factorization over real field R. On the first version, the primes are obtained from doubling and addition on elliptic curve points that are computed modulo composite number which is resulting as output of the CFs algorithm with the input r. Whereas, the primes, on the second version, are got directly from applying the CFs algorithm with r as input. The successful computation of the scalar multiplication kP on the elliptic curve E modulo primes are determined. The computational complexities of extended elliptic curve factorization versions are determined using the counting operations. These operations are elliptic curve and finite field operations. New numerical results on two versions are computed as study cases. The elliptic curve factorization algorithm over R (ECF-R) with two versions, is more efficient for factoring-based cryptography in comparing to the original ECM.

The paper focuses on the sufficient conditions for oscillatory property to the nonlinear impulsive differential equation(IDE) of the second order with damping term. We submitted a suitable impulsive conditions with the nonlinear equation. The obtained new results in this article generalize and extend some modification results to linear (IDEs) with damping term in the references. We have been given illustrative example to apply the conditions in the main results.

In this paper, we study the relationships among fuzzy (compact, pre-compact, α-compact and pα-compact) subspaces; also we will discuss the relationships between fuzzy (compact, p-compact, α-compact and pα-compact) spaces and fuzzy (compact, precompact, α-compact and pα-compact) subspaces.

Rough set theory had been proposed by Pawlak in the early of 1982. The theory is a new mathematical tool to deal with vagueness and imperfect knowledge. In this paper, we study neighborhoods for vertices of graphs with length that at most 2 edges. A new binary relation induced from a simple graph is defined and more properties of star definability which based on reflexive and transitive relation will be discussed. So, we investigate N-star lower and N-star upper approximations, for every subset B of a set of vertices V of a graph G. The relationship between the star set and independent set will be discussed.

Let G = (V(G), E(G)) be any connected simple graph and S be any subset of V(G) such that the cardinality of S is n – 1, n ≥ 3. The maximum distance between a vertex ν, ν ∈ V(G) and S(S ⊆ V (G) is the maximum distance between ν and u for all u ∈ S such that the vertex ν is not belong to S, that is:${d}_{max}(v,S)=max\{d(v,u):u\in S\},|S|=n-1,3\le n\le p,v\notin S$.

The maximum polynomial "M_n – polynomial" of G which denoted by M_n (G;x) and defined by:${M}_{n}(G;x)=\displaystyle {\sum }_{k=m}^{{\delta }_{\max }(G,n)}{C}_{n}(G,k){x}^{K}$, where m = min{d_max(ν,S),ν ∈ V – S, S ⊆ V} and C_n(G,K) be the number of pairs (ν,S), S ⊆ V(G), |S| = n – 1,3 ≤ n ≤ p, p = |V(G)| such that d_max(ν,S) = k, for each m ≤ k ≤ δ_max(G,n) and δmax (G,n) = max_u∈V{d_max(u,S)}.

In this paper, we find the M_n –polynomial and Hosoya polynomial for general thorn path and obtained some results.

In this paper, a numerical algorithm proposed by composing the Aboodh transform (AT) and Adomian decomposition method (ADM) and it has been named (ATADM). This algorithm is tested for solving some models of nonlinear problems. The modification gives robust tool for large size of enumerations. The obtained results of comparing approximate solution with exact solution for this scheme appeared high accuracy and efficiency for solving nonlinear problems.

The present paper focuses on the geometry of Wyle's tensor of nearly cosymplecticb manifold. Inbparticular, the flatnessb properties of Wyle's tensorb were traded. These propertiesb facilitated us tob identifyb the necessaryb and sufficient conditionb for nearly cosymplectic manifoldb to be an Einsteinb manifold.

In this paper we development of the complementary method to Solve Fractional Linear Programming Problems (FLPP), Instead of taking the Numerator and denominator elements and set them in in tables as D1 and D2, then calculating its value and the value of (Ze), hence we could minimize the tables and calculations in this method quickly and with fewer tables.

In this paper, we investigate two stress-strength models (Bounded and Series) in systems reliability based on Generalized Inverse Rayleigh distribution. To obtain some estimates of shrinkage estimators, Bayesian methods under informative and non-informative assumptions are used. For comparison of the presented methods, Monte Carlo simulations based on the Mean squared Error criteria are applied.

The purpose of this paper is to find best multiplier approximation of unbounded functions in L_p,ϕm –space by q-Bernstein-Kantorovich Aperator, in terms of the modulus of smoothness of one order using Korevkin Theorem.

In this article, we introduced a new concept of mappings called δZA - Quasi contractive mapping and we study the K*- iteration process for approximation of fixed points, and we proved that this iteration process is faster than the existing leading iteration processes like Noor iteration process, CR -iteration process, SP and Karahan Two- step iteration process for 𝛿 − quasi contraction mappings. We supported our analytic proof by a numerical example.

Support vector regression, especially, v-support vector regression (v-SVR) has been applied in several real problems. However, it is usually needed to tune manually the hyperparameter. In addition, v-SVR cannot perform feature selection. Nature-inspired algorithms were used as a feature selection and as an estimation for hyperparameter. In this paper, the Harris hawks optimization algorithm (HHOA) is proposed to optimize the hyperparameter of the v-SVR with embedding the feature selection simultaneously. Experimental results, obtained by running on two datasets, show that our proposed algorithm performs better than other methods, in terms of prediction, number of selected features, and running time. In addition, the HHOA's experimental results confirm the efficiency of the proposed algorithm in improving prediction performance and computational time compared to other nature-inspired algorithms, which show case HHOA's ability to search for the best hyperparameter values and to select the most informative features for prediction tasks. Therefore the HHOA may likely be ideal for defining the data relationship between input features and the target variable as opposed to other algorithms. In other real applications this is highly effective in making predictions.

Legendre polynomials (LPs) basis on the interval I = [-1;1] have been introduced and their properties are studied. Legendre polynomials with Gaussian integration method (GIM) are used to solve the initial value problems (IVPs) of third-order ordinary differential equations (ODEs). The aim of this work is to study the numerical solution of IVP which is widely applicable in the fields of engineering and science using Legendre base. The implementations have been discussed to demonstrate the validity and applicability of the technique of collections and variational methods which compared with the numerical results that obtained by classical RK and modern direct RKD numerical methods. Finally, the numerical results show the high accuracy and efficiency of the proposed method.

Limited dependent variable models, including truncated regression models, have traditionally been estimated by the method of maximum likelihood. The conventional optimization algorithms; which is known as Quasi-Newton algorithm namely BFGS Quasi-Newton algorithm is used to reach the optimum values for estimated parameters. In this paper, the nature-inspired algorithm is employed to improve the numerical optimization algorithms to better estimation. Our Monte Carlo simulation results suggest that our proposed improving can bring significant improvement relative to others, in terms of mean squared error and prediction mean squared error.

This paper is a summarized study of a soft transitivity and soft sensitivity of a soft continuous mappings on a soft topological spaces, where this study was confined to the purely soft topological aspect. Also, we discuss some basic soft topological techniques used soft-orbitity and soft-periodicity of a soft-point. On one hand, introduced a soft transitivity of a soft continuous mappings and provide a simplified overview of results on the topic, but on the other hand, it covers some of the recent developments. Finally, we introduce a new soft topology related to the soft transitivity of a soft continuous mappings on a soft compact soft set and the quest of soft density of soft-orbitity (soft density of periodicity) and using these notions, which are main results of our paper.

In this paper, we present a new iterations scheme for△ - convergence theorems of asymptotically and multivalued nonexpansive mapping in𝐶𝐴𝑇(0) spaces under the Fibonacci sequence

Some new concepts of grill nano topological structures throughout this paper are presented and studied. We generalize the famous closure operators that can be induced by binary operations. Some basic investigations for proposed structures are discussed. In addition, the connection between rough sets and grill set theory can be illustrated via some numerous examples. Finally, a comparison between proposed approaches and other studies is established.

Nuclear structure for even-even ¹³⁰Ba isotope have been investigated. They examined carefully with IBM1 and IBM2. Low lying energy levels for even even positive parity states, reduced electric quadruple transitions probabilities B(E2), branching ratios, reduced magnetic dipole transitions probability B(M1), reduced electric monopole transitions probability B(E0), and mixing ratio X(E0/E2) have been studied.

In the framework of IBM1 noted the competition between the two parameters (a₀ and a₂) in ¹³⁰Ba isotope was the increases of a₀ associated with decreases of a₂ which mean that the γ-unstable features in IBM2 χ_π and χ_ν were (-1.3 and 0.7) which signified similarity with IBM1 expected.¹³⁰Ba isotope described to be transitional nucleus, transitional between SU(3) and O(6) features.

The existing investigation explains the consequence of irradiation of violet laser on the optic properties of (CoO₂) films. The film was equipped by the utilization of semi-computerized spray pyrolysis technique (SCSPT), it is the first time that this technique is used in the preparation and irradiation using a laser in this technique. From the XRD analysis, the crystalline existence with trigonal crystal system was when the received films were processed by continuous violet laser (405 nm) with power (1W) for different laser irradiation time using different number of times a laser scan (0, 6, 9, 12, 15 and 18 times) with total irradiation time(0,30,45,60,75,90 min) respectively at room temperature. The optic properties of CoO₂ thin samples was struck by light of violet laser. The parameters such as the absorbance, coefficient of absorption coefficient of extinction refractive index, optic conductivity, the realε_1 and imaginaryε_2part of the dielectric constant of the films rises subsequently by laser irradiation, only the transmittance was decremented with laser ray of light. The optic energy gap was reduced from (1.98eV) without irradiation to (1.52eV) and subsequent laser irradiation, and there is a great alteration of optical energy gap values for photovoltaic (PV) utilization. As the results showed that the laser irradiation method has a clear change in the optical properties with less time and energy than the traditional annealing methods, this is the aim of the study.

Wheat and rice are among the main ingredients on which the Iraqi populations depend. The important part of this is detected knowledge the uptake radionuclide in this cereal, no less in admiration of any personal health harmful. In this study, we measured the concentrations of naturally occurring radioactive nuclides in cereals and the corresponding soil collected from agricultural fields in Al Shamiyah, Al- Diwaniyah governorate in Iraq using nuclear detector of tracks (CR-39). The mean activity concentration of uranium (ppm) in soil, wheat and rice samples were found to be 1.18 ± 0.19, 0.02 ± 0.001 and 0.88 × 10^-2 ± 0.00085, respectively. Factors of transfer from soil-to- cereals were limited to be 0.012 and 0.017 for wheat and rice. The results of TFs of ²³⁸U were found to be in agreement with previous studies values, these results refer to radionuclides movement were very low in these soils. Results have been shown the uranium concentration to be less than permissible limit (11.7 ppm) proposed by UNSCEAR. On the other side, results noticed there are no pose significant threats to health of human, the edible cereals being safe to consume.

The existing investigation explains the consequence of irradiation of red laser on the optic properties of (CoO₂) films. The film was equipped by the utilization of semi-computerized spray pyrolysis technique (SCSPT), it is the first time that this technique is used in the preparation and irradiation using a laser in this technique. From the XRD analysis, the crystalline existence with trigonal crystal system was when the received films were processed by continuous red laser (700 nm) with power (>1000mW)for different laser irradiation time using different number of times a laser scan (0, 6, 9, 12, 15 and 18 times) with total irradiation time(0,30,45,60,75,90 min) respectively at room temperature. The optic properties of CoO₂ thin samples was struck by light of red laser. The parameters such as the absorbance, coefficient of absorption coefficient of extinction refractive index, optic conductivity, the real_1 and imaginary_2part of the dielectric constant of the films rises subsequently by laser irradiation, only the transmittance was decremented with laser ray of light. The optic energy gap was reduced from (1.91eV) without irradiation to (1.57eV) and subsequent laser irradiation, and there is a great alteration of optical energy gap values for photovoltaic (PV) utilization. As the results showed that the laser irradiation method has a clear change in the optical properties with less time and energy than the traditional annealing methods, this is the aim of the study.

Image compression depends on data compression of digital images. Its central objective is to decrease the redundancy of the image data for reducing space and the cost of transmitting data in public communication channels. This research suggests a new compression technique based on the statistical rules. The proposed technique is one of the lossy compression techniques is based upon the statistics of the pixel values of the gray-scale image. The quality of these compressed images have been evaluated using some factors like the Image size before/after the compression process, Compression Ratio, (CR), and Peak Signal to Noise Ratio, (PSNR), Mean Square Error (MSE), and Mean Space Saving (MSS). Experimental results have demonstrated that the proposed technique provides sufficient higher compression with minimal to lose data.

It is well established that synthetic apertures of various shapes are superior to a single aperture in improving the overall performance of optical systems.

In this research, a set of elliptical synthetic obstructed apertures was used in place of the ellipse synthetic obstructed apertures that was used previously and the calculation of the point spread function to assess the performance of the optical system and reduce the diffraction values from it previously, according to the results, an improvement was observed in the optical system with array of elliptical synthetic obstructed apertures.

Currently, manual system is being used for the matches booking is too old which need great time and efforts from both of the customers whom used to wait in long queues to get their tickets and the stadium staff whom also spend a lot of time trying to organize the booking process. In addition, cash payment with all of its disadvantages is accepted. The proposed mobile ticketing system will provide an easy way for users to booking their e-tickets for their favorite matches from anywhere and anytime, only it needs to a personal computer or a smartphone and connect to an internet. Therefore, without the need to wait in long queues for a long time. The user will get his e-ticket in a way that will gain a lot of time and efforts for both of the users and the staff. In this study, "the Method of Booking e-tickets for Iraqi Stadiums using the Smartphone" will be introduce. The study has been implemented using five major steps. The prototype will go through Awareness of the problem that will happen through the interview with the person who is in charge at stadium, and the problems that you are trying to solve as well. The main interface of the system will contain some of the box to enter the information about the customers, thus they can make the booking easily. Development, evaluation are the last steps to finalize the system usefulness to be implement in real life. Nowadays, the mobile becomes the most important thing that plays main role in many activities that we need it in daily life. Therefore, this study will depend on a mobile phone application, which is expect to give ease and effectiveness to the users and the administrator's requirements in saving time, cost and efforts.

The association between galaxies is a phenomenon frequently occurring in the universe. Systems called Polar Ring Galaxies (PRGs) can be built for certain interactions. These structures consist of a galaxy known as a host and a ring of gas and stars surrounding a plane nearly perpendicular to its main axis. This research has contributed to the creation of a first library of N-body simulations, to study the parameters required to construct PRGs. A library of this kind is continuously expanding with new simulations based on these first findings. The inherent secular processes of isolated galaxies cannot give rise to this PRG geometry. Such systems are (i) created by galaxy interactions or (ii) by the introduction of cold gas from interstellar filaments within a galaxy. The most popular mechanisms are thought to be (i), and we are interested in this project, particularly where gas from one galaxy to another is introduced, without the need for a fusion. For formation of interaction, orbits with particular geometries are required in order to attach matter to form a polar ring. We review various mass ratios, inclinations and orbital energies in our society. The database which will be developed with the simulation results will contribute to future research on the interaction between galaxies, especially polar rings.

In this paper, the effectiveness of using random forest algorithm in the big data is studied. The reason for choosing this algorithm is because of its effective results in many previous studies, so it was chosen. The random forest algorithm was applied to the big data Internet of Things (IoT) dataset, with size 150,000 instances. After applying the algorithm, it gave an Accuracy score of 99.976%, and this indicates the effectiveness of the random forest algorithm in the big data. This result made the researcher search for one of the ways that increases the value of Accuracy, knowing that it is an excellent result. And use a filter to remove frequent values, and this helps reduce data volume and keep related data. After applying the filter with the random forest algorithm, the Accuracy value appeared at 99.998%, which indicates that it improved the random forest algorithm's performance in the big data.

The manufacturing sector is facing a challenge in this 21^st century to continue developing their business by applying a new and innovative production technology and system. This is to help the novel ways of manufacturing process to move forward, where, the Machine Design will feature and compile the newest product line with an inventive technology to keep modernized techniques at the top of mind for our OEMs, end-users, integrators, and the entire supply community. This research paper will explore how the simulation derived model of Mechatronic could manage the most complex scheme of the machinery profile with a systematic approach by understanding the concept with precise machine design actions, dynamic behavior, and effective interaction with the various components of the machine. Mainly, the Mechatronic engineers will unite the mechanics, and electronics principles and compute them to generate more economical, a simpler, and reliable system.

The Mechanical Engineering essence is the understanding of all the available resources, their effective utilization, and making use of the law of nature to help, gain and benefit the entire humanity. Mechanical Engineering is the applied science using scientific knowledge and procedures as the means to accomplish a specific practical and useful results. It is related to the sense that involves a proper understanding of all the scientific principles and effectively applying them to attain the designated goal. The machine design in mechanical engineering is the most crucial section of engineering, and it deals with the design, conception, refinement, development of machines and component application together with the mechanical apparatus of every kind.

In the professional engineering, the main concern is to obtain the requisite solutions to all the practical problems in the machinery production. The solutions should reflect the knowledge, understanding and application of the underlying technology and science. However, normally the mere understanding is not sufficient. The related empirical knowledge together with engineering judgment become the most prerequisite. For instance, no scientist can entirely understand electricity. However, it does not prevent any electrical engineer from creating highly useful and functional electrical devices. Likewise, no scientist can fully understand metal fatigues and combustion procedures, yet, the mechanical engineers utilize the knowledge and insight available to generate highly useful and functional combustion engines. When more scientific solutions are accessible, engineers can devise better explanations and clarifications to practical problems. This study tries to analyze and evaluate the perception and usefulness of AM- additive manufacturing systems and technologies to understand machine elements, product design and its development.

The COMOSOL multiphysicsis used to design various optical systems, including the design of the acousto-optic modulator system. Its work depends on the special inputs of the program, such as the characteristics of the laser used and the frequencies of the sound waves. A square modulator was designed with dimensions 3x3 mm, and a quartz crystal was used, in which the interaction of light and sound occurs. Different number of orders diffraction are generated called the Bragg angle, and their number varies with different inputs. The modulator is created by entering the value of the radio frequency up to 100 volts. Through our results, the efficiency increases at the frequency of 400 kHz after changing the frequencies of 200, 300 and 400 kHz. The values of the stress are: 1.24 × 10⁶Pa, 1× 10⁶Pa, 3.8× 10⁶Pa, and the estimated shift is about 0.7, 0.4 and 0.9 mm, there were three frequency values considered: 200, 300, and 400 kHz. respectively. The far field shape show two orders are appeared at 200 kHz and 300 kHz frequencies they are: zero order and first order but they are different in the value of Bragg angles but in 400 kHz shown approximate three orders, they are: zero, first, and new generation of second order with the different in the value of Bragg angles.

SDD basis sets were used in current work together with the hybrid B3LYP functional to investigate of suggested platinum metal complex. The results showed the complex under study likes the cisplatin complex in many of it is properties, they have large band gap with low electrochemical hardness and electronic softness. Based of cis-platin, the substitute of iso-indene rings in place of amine groups in cis-platin unaffected on the geometrical parameters of bonding the central platinum metal with chlorine atoms and the ligands, the suggested platinum complex keeps the coordination of metal complex with values of frontier molecular orbitals close to those for cisplatin. π →π^* transition of states were appeared in the behavior of absorption spectrum for the complex under study.

Tracking student attendance and location information are at the heart of a pervasive internet thing. Several approaches are used to identify student locations in the classroom, Infrastructure and increased services are considered expensive requirements and hardly meets the need for the required room-level location accuracy. An accuracy of specifying the student's location by Smart Entity (inertial sensors on hand) of improving the quality of service. Location information forms a core context to determine student location. The location of classroom access control using different parameters provides useful information and improves teaching and learning in the educational organization. Based on the recent IoT integration of smart entities and sensors, this paper uses new value-added proposals to monitor the actions of students inside the classroom location.

The importance of Graph Theory comes from being Combinatorics. It can study this subject and its relationship to the topological using plane graphs where they are embedded graphs. Also, its relationship to linear algebra which can study the using of matrices. This article describes the adjacency matrices of adjacent vertices of plane graphs and their duals by finding the formula of the adjacency matrix of some types of plane graphs and their duals.

This paper deals along the solutions numerical and presentence estimates As fractional equation as differential class, while the problem nonlinear part admits some distinct hypotheses. In particular, As precise parameter localization, the non-0 solution presentence is recognized requiring the sub linearity nonlinear part at infinity and origin. Furthermore, theoretical and numerical examples of applications are provided.

We investigate a chemostat model that contains interaction between two bacteria species, the aerobic species, and a facultative anaerobic species. The competition is restricted on the dissolved oxygen where the aerobic species consumes the oxygen for growth, on the other hand, the facultative anaerobic species do not need the dissolved oxygen for growth. We found that the aerobic growth rate is more extensive compared to that of its competition, the anaerobic species. During our study of the chemostat system, we found three equilibria solutions. The first one is found at the initial dissolved oxygen concentration with the condition of both species washed out. The second equilibrium point is seen when both the dissolved oxygen and the aerobic species present, and finally, the third equilibrium point is found when the dissolved oxygen and the facultative anaerobic species present. We used MATLAB software to simulate these aforementioned three equilibria.

Local and global bifurcations of food web model consists of immature and mature preys, first predator, and second predator with the current of toxicity and harvesting was studied. It is shown that a trans-critical bifurcation occurs at the equilibrium point E₀, and it revealed the existence of saddle-node bifurcation occurred at equilibrium points E₁, E₂ and E₃. At any point, the occurrence of bifurcation of the pitch fork does not occur. However, Hopf bifurcation is carried out around positive equilibrium point only.