Journal of Kufa for Mathematics and Computer

Deep learning and machine learning are widely employed in various domains. In this paper, Deep Neural
Network (DNN) and Convolution Neural Network (CNN) are used to estimate the Instantons Frequency (IF), Linear
Chirp Rate (LCR), and Quadratic Chirp Rate (QCR) for Quadratic Frequency Modulated (QFM) signals under Additive
White Gaussian (AWG) noise and additive Symmetric alpha Stable (SαS) noise. SαS distributions are impulsive noise
disturbances except for a few circumstances, lack a closed-form Probability Density Function (PDF), and an infinite
second-order statistic. Geometric SNR (GSNR) is used to determine the impulsiveness of mixture noise for Gaussian
and SαS noise. DNN is a machine learning classifier with few layers that reduce IF, LCR, and QCR estimation
complexity and achieve high accuracy. CNN is a deep learning classifier that is built with multiple layers of IF, LCR,
and QCR estimation. CNN is more accurate than DNN when dealing with large amounts of data and determining
optimal features. The results reveal that SαS noise is substantially more damaging to IF, LCR, and QCR estimation
than Gaussian noise, even when the magnitude is modest, and it is less damaging when alpha is greater than one. After
training CNN for IF, LCR, and QCR estimation of QFM signals. The 2D-CNN model accuracy achieved 98.7603 and
1D-CNN is 75.8678 for ten epochs. DNN model accuracy achieved 37.5 for 1000 epochs. The accuracy of TFD
(spectrogram & pspectrum) for frequency estimation of QFM signals was 38.4254 by spectrogram and 38.6746 by
pspectrum.

The corona pandemic disrupted the educational process, especially in universities that use traditional
education. Universities were therefore obliged to move from traditional education to e-learning without adequate
preparations. The aim of this research is to analyze the students\' performance in the two educational environments and predict the result of any of them in the future. The k-means algorithm, an important data mining method, was used to analyze the results of the fourth-stage classes of five consecutive years of students from one Iraqi university\'s scientific departments. Four of these years were traditional education, while the last was e-learning to see whether the student\'s performance distribution is normal or abnormal. The results indicate a 100 percent of students’ success rate in eeducation, while the upper limit is 70 percent for the previous years. Moreover, the
average class rate increased to 75 percent compared to 62 in previous years. The decision tree has been
built based on a dataset created from the collected data to predict the distribution of both traditional
and e-learning with a 2% error tolerance. The study shows that using the exact mechanism in e-learning will give bnormal results. Therefore, the study recommends the need for good infrastructure, the preparation of efficient staff,
ncreasing students’ skills, and appropriate software platforms for an accurate assessment of students’ performance.

In this study, we devised 4-point implicit block (New 4pb) approaches that take advantage of second
derivatives. The aim provides is more accurate and quicker numerical solutions to first - order ordinary differential
equations (ODEs). Whereas the properties of the (New 4pb) method such as the order and zero-stability have been
discussed. After that, the approaches are applied to a collection of first-order (ODEs). In addressing the set of test
problems, numerical results clearly indicate that the newly proposed systems outperformed previous, well-known
existing methods.

With the increasing number of published books and the challenge of acquiring adequate research interest,
recommendation systems have developed as a key tool for assisting scholars by proposing relevant and valuable books
or articles automatically. Recommendation systems have the potential to enhance the accessibility and affordability of
books. A recommendation system already exists, but results may be inaccurate in addition to the two main problems of
RS: the cold-start problem and the data sparsity problem. In this work, aims to improve the precision of book
collaborative filtering through the application of semantic similarity to book summaries. Furthermore, the study seeks
to address the significant challenges associated with scalability and sparsity by employing effective techniques. The
proposed methodology comprises three stages: preprocessing, building the system, and evaluation. The technologies
used in the pre-processing stage included reduction and normalization. The construction system is divided into two
phases: semantic similarity and recommendation. The semantic similarity is done by using BERT for sentence
embedding and to calculate the similarity between sentences by cosine similarity. During the recommendation phase
by using CF based on KNN. In the evaluation stage, classification accuracy metrics had been used. The proposed
approach resulted in an enhancement of the accuracy of the book recommendation system, elevating it to 0.89 in
contrast to antecedent studies and based on a dataset of 271,000 book summaries. The results obtained from the
proposed approach were superior, as it circumvented issues encountered in preceding works, such as sparsity and
scalability, by using BERT with CF based KNN. Filtering the data using BERT and the KNN algorithm in the CF added
strength to the recommendation, which led to an increase in the accuracy rate.

In this paper, we study formula for the backward doubly fuzzy stochastic differential equations
(BFDSDEs), In the beginning, we study some basic concepts, definitions, and Hypotheses to obtain the numerical
scheme for BFDSDEs, as our scheme depends on the partition of interval [0, T]. In our work, we prove that under
Lipschitz conditions, the approximation solution for the backward fuzzy doubly stochastic differential equations
converges to the exact solution by using mean square error, and prove the existence and uniqueness of approximations solutions to BFDSDEs.

In this research will study the syndetic set in topological transformation group, that represents one of
the important sets in topological dynamics that Gottschak referred to in a book topological
dynamics. Relationship between syndetic set and translation (left-right- bilateral) provided, In right topological
transformation group have presented semi replete set and extensive set and referred to the relationship of semi
replete set and extensive set on the one hand, and their relationship with syndetic set on the other hand. Introduced
a new idea syndetic proximal point that depended on syndetic set and indicated to a relationship syndetic proximal
point with proximal point and extensive proximal point, and concluded a number of relationships and
theories.Keywords— syndetic set, topological transformation group, proximal point

Cardiomegaly is a condition characterized by an enlarged heart, which can be indicative of various
underlying health issues. Early diagnosis of this condition lessens the patient's repercussions. The paper gives a
thorough overview of the disease, its classifications, algorithms, and methods employed emphasizing the challenges
encountered in this field. Traditional methods of diagnosing cardiomegaly rely on medical imaging techniques such as
echocardiography or chest X-rays, which can be time-consuming and require specialized expertise to interpret.
However, recent advances in deep learning algorithms have shown promise in accurately identifying cardiomegaly and
its underlying causes from medical images. The use of deep learning algorithms in the diagnosis of cardiomegaly has
the potential to improve both the speed and accuracy of diagnosis, leading to better patient outcomes and more efficient use of healthcare resources. Moreover, deep learning algorithms can potentially identify subtle changes in heart size over time, allowing for earlier detection and treatment of cardiomegaly.

In this research, the Bayes estimator was derived based on Time censored data of the first type, and the
Failure censored data of the second type. Reliance has been made on extension of Jeffery prior information. Finally,
the simulation was used based on the MATLAB program and with different inputs to find the best estimator among
Maximum Likelihood estimator and Bayes estimators with extension that has the least mean percentage error.

This work considers the construction of the concept of distributive property for semimodules. Some characterizations of this property, with some examples are given. Some conditions on semiring or semimodules (like
subtractive, semisubtractive, cancellative, and k-cyclic) are required to obtain interesting results. The main results are:
Any subsemimodule and factor semimodule of a distributive semimodule is distributive. Moreover, weakly distributive,
is also, introduced and investigated. It is found that the semimodule is distributive if and only if each subsemimodule is
weak distributive. Taking advantage of the supplemented concept to find some properties of distributive semimodule.
Finally, the summand sum and summand intersection properties for distributive semimodules with some conditions are valid.

Supervised Machine Learning algorithm has an important approach to Classification. We are predicting
the deal type of the Iris plant using various algorithms of machine learning. Iris plants are determined by numerous
factors such as the size of the length and width of the property. A horticultural skill announces that some of the plants
are different in some physical appearances like size, shape, and color. Hence it is difficult to recognize any species.
Versicolor, Setosa, and Virginica have three identical subspecies of The Iris flower species. This paper uses machine
learning algorithms to recognize all classes of the flower with an accuracy degree of %100 for KNN, %95 for RF, %97
for DT, and %98 for LR. The Iris dataset is frequently available, and it is implemented using Scikit tools. and build the
prediction model for Plants. Here, algorithms of machine learning such as Logistic Regression (LR), Decision Tree
(DT), K Nearest Neighbor (KNN), and Random Forest (RF) are employed to construct a predictive model.

This study examines the various ways that fractional Laplace transform can be used to solve three different
kinds of mathematical equations: the equation of analysis of electric circuits, simultaneous differential equations, and
the heat conduction equation. This article how to use the fractional Laplace transform to calculate heat flow in semiinfinite
solids
in
the
context
of
heat
conduction.
The
answers
that
are
developed
offer
important
information
about
how

temperatures

vary across time and space. The essay also examines how to analyse electrical circuits using the
Fractional Laplace transform. This method allows researchers to measure significant electrical parameters including
charge and current, which improves their comprehension of circuit dynamics. Practical examples are included
throughout the essay to show how useful the Fractional Laplace transform is in various fields. As a result of the answers
found using this methodology, researchers and engineers working in the fields of heat conduction, system dynamics,
and circuit analysis can gain important new knowledge. In conclusion, this study explains the applicability and
effectiveness of the fractional Laplace transform in resolving a variety of mathematical equations. It is a vital tool for
researchers because it may be used in a wide range of scientific and engineering areas.

The main purpose of this research is to study the degree of the best multiplier approximation of monotone
unbounded functions in ????????,???????? (????) −space, where ???? = (????, ????) by spline polynomials in terms of averaged multiplier
modulus smoothness ????(????, ????)????,???????? using some definitions and theorems necessary for this.

Nowadays, it is quite usual to transmit data through the internet, making safe online communication
essential and transmitting data over internet channels requires maintaining its confidentiality and ensuring the integrity of the transmitted data from unauthorized individuals. The two most common techniques for supplying security are cryptography and steganography. Data is converted from a readable format into an unreadable one using
cryptography. Steganography is the technique of hiding sensitive information in digital media including image, audio,
and video. In our proposed system, both encryption and hiding techniques will be utilized. This study presents encryption using the S-DES algorithm, which generates a new key in each cycle to increases the complexity of the algorithm detection. An additional shared key between the sender and the receiver is added which is applied before starting the encryption process, that key must be hex-decimal in order to increase the level of security and give enough time to delay the guessing of the secret text by the attackers. The secret message data is concealed using one of the two techniques:
either least significant bit (3-LSB) steganography or hiding in green and blue bits. To expedite the concealment process, the cover image is enhanced by applying a median filter, the median filter removes noise from the image while preserving its details. Finally, comparing the results of the two methods to determine which is better for the cover image in terms of PSNR metrics and hiding process time.

Because, the new knowledge put every new structure in category theory. So, became a source of interest
for many researchers, to put every new structure in category theory. This motivates us to put the new structures of
semibornological group in category. Furthermore, new classes of semibornological group was constructed, which it is
a semibornological group with respect to S-bounded maps and semibornological groups with respect to S**-bounded
maps. The main important results, every semi bornological group is S-semi bornological group and S**-semi
bornological group but the converse is not true. Also, we gave the certain condition for any codomain of S-semi
bornological group to be S**-semi bornological group. Additionally, every left (right) translation is S-bornological
isomorphism and S**-bornological isomorphism, every bornological isomorphism is S-bornological isomorphism and
S**-bornological isomorphism.

This article explores the properties and theorems pertaining to subtractive and distributive semimodules.
The focus is on understanding the relations between these characteristics and their implications within the context of
semimodules. The investigated propositions establish conditions for distributivity in semimodules. It is shown that under certain circumstances, the preimages of subsemimodules under homomorphisms exhibit specific additive properties.
Furthermore, the study introduced definitions and propositions related to supplements, principally supplemented
semimodules and H-supplemented semimodules. The findings reveal the importance of supplements in understanding the structure and properties of semimodules, particularly in relation to their distributive nature.

A project's aim is to investigate use the complex of characteristic '0' in the event of a partitioning
(4, 4, 3) using the idea of mapping Cone and the concepts divided power the place polarization, illustrations, and
Capelli (1) in this partitioning.

The main purpose of this paper is to study the application of Weyl module and it’s resolution in the case of two rows which way be specified in the partitions (7, 5) and skew-partition (7, 5)/(1, 0), using the homological way
(i.e. the contracting homotopy, place polarization.

In this paper, we present a novel transform namely INEM – Transform , involving a lot of potential new
or known transform basic characteristics of the new transform were examined in this work as special cases., authors
first derived the INEM – transform of basic mathematical functions ,theorem of linearity ,theorem of derivatives and
the definition of inverse formula .a novel transformation used to address specific initial value problems of higher order
,some illustrative examples, and use of application in two applications: finding the blood glucose concentration and
finding the aortic pressure presented in this work.

The purpose of this paper, is to define and discuss a representation on an n-Bi-Hom Γ-Lie algebra and
give some results about them.

Statistical properties of the energy-like statistic under bivariate Sine-Model circular distribution and
chord circular distance is presented in this paper. Simulation study is consider as well to examine the properties that
we computed by comparing the true expected value and variance of the Sine-Model with the estimated expected value and variance under different sample sizes and different values of the parameters using R-Studio software.

In this study, we define the w-expansive property of generic non-autonomous discrete dynamical systems. We also show how the w-expansive feature is preserved under conjugate, inverse limits, and iterate. In addition, we discuss the relationship between the w-expansive and shadowing properties in generic non-autonomous discrete dynamical systems.

Steganography is the practice of secretly encoding information into another medium (called a cover media) such that
its existence cannot be identified. Steganography is the method that is utilized to successfully do this task. Through the use of digital image steganography, one is able to achieve the capacity of secure communication, which is vital in the bulk of the applications that are now being created. The use of steganography is applicable in a wide variety of advantageous settings. Its ascent to the forefront of current security systems may be attributed to a confluence of factors, including a phenomenal rise in processing power and a heightened awareness among individuals of the need of safeguarding their personal information. When it comes to the creation of a steganographic method, the most significant challenge that must be surmounted is finding the optimal balance between quality and quantity. The method is distinguished from linked systems like encryption and watermarking by its ability to embed information, as well as by the fact that it cannot be seen by the human eye. This article presents a thorough examination and analysis of some contemporary steganographic methods that are regarded as state-of-the-art approaches. In addition, we have included an in-depth discussion of the most important steganographic technologies now available. Recent steganographic techniques that are based on deep learning have been enhanced, which has enabled the resolution of issues that were previously present.

Steganography is the practice of secretly encoding information into another medium (called a cover media) such that
its existence cannot be identified. Steganography is the method that is utilized to successfully do this task. Through the use of digital image steganography, one is able to achieve the capacity of secure communication, which is vital in the bulk of the applications that are now being created. The use of steganography is applicable in a wide variety of advantageous settings. Its ascent to the forefront of current security systems may be attributed to a confluence of factors, including a phenomenal rise in processing power and a heightened awareness among individuals of the need of safeguarding their personal information. When it comes to the creation of a steganographic method, the most significant challenge that must be surmounted is finding the optimal balance between quality and quantity. The method is distinguished from linked systems like encryption and watermarking by its ability to embed information, as well as by the fact that it cannot be seen by the human eye. This article presents a thorough examination and analysis of some contemporary steganographic methods that are regarded as state-of-the-art approaches. In addition, we have included an in-depth discussion of the most important steganographic technologies now available. Recent steganographic techniques that are based on deep learning have been enhanced, which has enabled the resolution of issues that were previously present.

we introduce the notion of translation bifuzzy , bifuzzy extensions , translation bifuzzy of bifuzzy ???? -subalgebra , bifuzzy ???? -ideals on ???? -algebra and investigate some of their properties, we discussion the R-intersection , the ????-intresection, the R-union , the P-union of any sets of translation bifuzzy ????-subalgebra , we will present some results on images and pre-images of translation bifuzzy ????- subalgebras and translation ????-ideals of ????-algebra and we introduce the notions of Cartesian product of bifuzzy ???? subalgebras and bifuzzy ideals in a ???? -algebra.

in this paper we introduce the notions (L-????ℎ???????????????????????????? ????????????????????????????????, two – sided limit shadowing, negative
???????????????????? ????ℎ???????????????????????????? ????????????????????????????????, ???????????????????????? ???????????? – ???????????????????? ???????????????????? ????ℎ???????????????????????????? ) for fuzzy dynamical systems and prove that
properties (fuzzy ????ℎ???????????????????????????? ????????????????????????????????, fuzzy L-????ℎ???????????????????????????? ????????????????????????????????, fuzzy two – sided limit shadowing) are
invariant under fuzzy ???????????????????????????????????????????? ????????????????????????????????????????????.

Scalar multiplication is the fundamental operation in the elliptic curve cryptosystem. It involves
calculating the integer multiple of a specific elliptic curve point. It involves three levels: field, point, and scalar
arithmetic. Scalar multiplication will be significantly more efficient overall if the final level is improved. By reducing
the hamming weight or the number of operations in the scalar representation, one can raise the level of scalar
arithmetic. This paper reviews some of the algorithms and techniques that improve the elliptic curve scalar
multiplication in terms of the third level.

ancer is one of the top causes of death globally. Recently, microarray gene expression data has been used to aid
in cancers effective and early detection. The use of machine learning techniques in biomedicine and bioinformatics to categorize cancer patients into high- or low-risk groups was investigated by numerous research teams. It is necessary that machine learning tools can recognize important features in complex datasets. Here we present a machine learning approach to cancer detection, and to the identification of genes critical for the diagnosis of cancer .We used the Support Vector Machine (SVM), Random Forest (RF), K-Nearest Neighbor (KNN), and Gradient Boosting (GB) that provide results that are more accurate than those of current models.Each model's accuracy, including SVM, KNN, RF, and GB, was (97.41%, 89.3%, 88.1%, and 85.7%), respectively. The SVM has the highest precision among machine learning algorithms. By creating a machine learning-based predictive system for early detection, our findings can help to decrease the prevalence of cancer disease.