Mustansiriyah journal of pure and applied sciences

Neural network algorithms are similar in structure to the human mind, they work in the same way as the mind works in transmitting, processing and analyzing information, reaching conclusions, discovering patterns and predictions and we can apply some of what the natural mind applies, although scientists are still discovering more about it until now and have not met all its details. The nature of the algorithms of these networks contributed to them being the most widely used in the field of artificial intelligence, as they aim to simulate human intelligence and give the machine some of the capabilities of the human mind. In this research paper we presented the study of the gradient descent algorithm and the gradient descent algorithm with momentum on a model of an objective function and by comparing their results it was shown that the gradient descent algorithm with momentum leads to better and faster learning and with less repetition compared with the gradient descent in reaching the optimal value and the results were calculated using Python. Keywords: Optimization Algorithm, Algorithm of Neural Network, Cost Function.

For a fuzzy topological space, we aim to investigate a class of fuzzy covering function which we call the -local covering dimension function. We also examine the relationships between fuzzy -covering dimension function under the conditions of fuzzy -separation axioms and fuzzy -connected spaces. Finally, we give a number of characterizations for ????-covering dimension and fuzzy ????- local covering dimension by the use fuzzy countable sets provided a number of properties

This study presents a new conjugate gradient formula (CGM), which is obtained by fulfilling two conditions, firstly the conjugate property and secondly the descent property, in order to address the issue of unconstrained optimization. The gradient, which is the initial derivative of the objective function, is a continuous Lipchitz work and the objective function is differentiable. Using a new variable that serves as the gradient for the objective coefficient function, to create a new course of action based on the old variable and to validate the effectiveness of the new CDM, the table with total iterations and job evaluation was used to display the results of our new methodology using the MATLAB application

Many researchers related to the degree of unconstrained approximation to constrained approximation, and proved the inequality: For a continuous function on a closed interval we have ( ) ( )( ) ( )
where is a positive constant. The converse of the relation ( ) is not achieved, so we will obtain the converse of the relation ( )under some conditions on which belonging to quasi normed spaces.

Neural networks are tools for parallel computations of functions with several variables, it is a linear computation of non-linear functions that we are call activation functions. In our paper we deal with one hidden layer feed forward neural network.
We have two problems with neural networks approximation, the first is the density problem concerns. With the condition for the approximated function to approximate by the neural networks. In previous works on approximation using neural networks, the weights are different for each input. This makes engineering applications very difficult.
In this work we approximate any bounded function on for by a forward neural network and find the degree of the best approximation by this neural network using the k’ th order of smoothness. Then we connect neurons number and the degree of the best approximation.

In this work, we present new concept which is y-closed-pseudo-projective module (briefly, YCP-projective module). This work which is generalization of pseudo-projective modules. We have provided some characteristics and descriptions of those concepts. Semi-simple modules have been characterized in terms of YCP- projective modules. We have shown the relationships of YCP-projective with other concepts, including a Co-Hopfian, directly finite modules.

Recently, cybersecurity breaches have become more common, with varying levels of impact ranging from simple to major losses of financial resources or data. The network infrastructures are the main goal of the malicious activity to compromise confidentiality, integrity, and availability (CIA) of information security. The network devices produce a large number of logs, making the handling of these logs very important because they serve to record all activities and events that take place on the network’s devices and applications to detect and prevent abnormal behaviors. Network security monitoring is a process used to monitor network devices and their traffic to detect security vulnerabilities, threats, and suspicious activities. Organizations are using network security monitoring to quickly detect and respond to cybersecurity threats. Various methods are used to protect network devices, like antivirus, firewalls, intrusion detection systems (IDS), and intrusion prevention systems (IPS), which typically operate independently. For that reason, attacks cannot be identified unless logs and events from different devices and applications are correlated and managed from a centralized location. Security information and event management (SIEM) addresses this issue by offering the capability to increase the level of information security and data protection through centralized log management for network devices. This paper presents a survey of network security monitoring techniques, encompassing their functionality, contents, and tools. Traditional tools, intrusion detection and prevention systems, and SIEM are some of these tools. In addition, the paper introduces SIEM as the most common and advanced security tool, highlighting its functionalities and capabilities.

In this paper, is derived the reliability of n-cascade stress-strength system model based on the Gumbel Type- 2 Distribution (GT-2) with unknown parameter λ and known parameters β , for probability of n- components having strengths Y between two stresses X and Z .In the Gumbel Type- 2 Distribution ,there are six methods of parameters and this system reliability estimators where discussed by using the Maximum Likelihood, Moments Method, Least Square Method, Weighted Least Square Method , Regression and Percentile ,based estimators on the simulation technique , these estimates are compared by the mean square error criteria for both small, medium and large samples .It has been concluded that the maximum likelihood estimator performs better than all the options considered.

In this essay, we propose a new family for inverse of Hessian matrix which based on
definition of convex combination class and on modified symmetric rank one update (MSR1) with
( DFP) update and upgraded BFGS (MBFGS) revision for the inverse of the Hessian matrix and
the properties of symmetric and positive definite will be shown and proved as well as the theoretical
and numerical global converge is proposed , numerical experiment on eight functions are presented
in a table.

In this work a new method called Sequences method used to establish new diagram which called -abacus with four different movements, namely . Then, a new rule constrict to find es-abacus diagram constrict in case from -abacus diagram in case . Further, several examples are given to illustrate the new method.