Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

There has been a growing interest in the use of chaotic techniques for enabling secure communication in recent years. This need has been motivated by the emergence of a number of wireless services which require the channel to provide very low bit error rates (BER) along with information security. This paper investigates the feasibility of using chaotic communications over Multiple-Input Multiple-Output (MIMO) channels by combining chaos modulation with a suitable Space Time Block Code (STBC). It is well known that the use of Chaotic Modulation techniques can enhance communication security. However, the performance of systems using Chaos modulation has been observed to be inferior in BER performance as compared to conventional communication

This study proposed control system that has been presented to control the electron lens resistance in order to obtain a stabilized electron lens power. This study will layout the fundamental challenges, hypothetical plan arrangements and development condition for the Integrable Optics Test Accelerator (IOTA) in progress at Fermilab. Thus, an effective automatic gain  control (AGC) unit has been introduced which prevents fluctuations in the internal resistance of the electronic lens caused by environmental influences to affect the system's current and power values ​​and keep them in stable amounts. Utilizing this unit has obtained level balanced out system un impacted with electronic lens surrounding natural varieties.

Longitudinal data is becoming increasingly common, especially in the medical and economic fields, and various methods have been analyzed and developed to analyze this type of data.

In this research, the focus was on compiling and analyzing this data, as cluster analysis plays an important role in identifying and grouping co-expressed subfiles over time and employing them on the nonparametric smoothing cubic B-spline model, which is characterized by providing continuous first and second derivatives, resulting in a smoother curve with fewer abrupt changes in slope. It is also more flexible and can pick up on more complex patterns and fluctuations in the data.

The longitudinal balanced data profile was compiled into subgroup

Abstract
             In this research will be treated with a healthy phenomenon has a significant impact on different age groups in the community, but a phenomenon tonsillitis where they will be first Tawfiq model slope self moving averages seasonal ARMA Seasonal through systematic Xbox Cengnzla counter with rheumatoid tonsils in the city of Mosul, and for the period 2004-2009 with prediction of these numbers coming twelve months, has found that the specimen is the best representation of the data model is the phenomenon SARMA (1,1) * (2,1) 12  from the other side and explanatory variables using a maximum temperature and minimum temperature, sol

Blockchain represents a new promising technology with a huge economic impact resulting from its uses in various fields such as digital currency and banking; malware represents a serious threat to users, and there are many differences in the effectiveness of antivirus software used to deal with the problem of malware. This chapter has developed a coefficient for measuring the effectiveness of antivirus software. This chapter evaluates the effectiveness of antivirus software by conducting tests on a group of protection programs using a folder containing an amount of data. These programs are applied to combat viruses contained in this folder. The study revealed that the effectiveness of antivirus software is as follows: AVG scored 0%,

The interest in art for young ages is seen as an obvious breakthrough and as revealing of psychological and health feelings in addition to emotions, and it is a treatment for those who suffer from behavioral disorders. The problem arose with the following question: What is the role of artistic expression in diagnosing behavioral disorders for primary school pupils? The aim of the research is to detect the behavioral disorders in the artistic expression of the female students' paintings from the teachers' point of view. The descriptive analytical approach was adopted as it is the appropriate method for identifying and estimating the characteristics and features related to people, places and things, and analyzing situations or phenomena as a

This paper interest to estimation the unknown parameters for generalized Rayleigh distribution model based on censored samples of singly type one . In this paper the probability density function for generalized Rayleigh is defined with its properties . The maximum likelihood estimator method is used to derive the point estimation for all unknown parameters based on iterative method , as Newton – Raphson method , then derive confidence interval estimation which based on Fisher information matrix . Finally , testing whether the current model ( GRD ) fits to a set of real data , then compute the survival function and hazard function for this real data.

A high-performance liquid chromatography method was employed for the quantitative determination of ascorbic acid (AA) which called vitamin C in three types of Iraqi citrus (orange mandarin and aurantium ) and to establish this goal , evaluation of ascorbic acid degradation is so important due to its significant criticality when exposure to ordinary atmospheric conditions. The chromatographic analysis of AA was carried out after their sequential elution with KH2PO4 ( as mobile phase) by reverse-phase HPLC technique with C8 column and UV detection at 214 nm. .Bad resolutions was appeared clearly for C8 column , so another alternative condition were carried out to improve the resolution by replacement of C8 by C18 column .Statistical treat