This study aims to classify the critical points of functions with 4 variables and 8 parameters, we found the caustic for the certain function with the spreading of the critical points. Finally, as an application, we found the bifurcation solutions for the equation of sixth order with boundary conditions using the Lyapunov-Schmidt method in the variational case.

Abstract

 The current research aims to identify the analysis of the questions for the book of literary criticism for the preparatory stage according to Bloom's classification. The research community consists of (34) exercises and (45) questions. The researcher used the method of analyzing questions and prepared a preliminary list that includes criteria that are supposed to measure exercises, which were selected based on Bloom's classification and the extant literature related to the topic. The scales were exposed to a jury of experts and specialists in curricula and methods of teaching the Arabic language. The scales obtained a complete agreement. Thus, it was adapted to become a reliable instrument in this

In this research, the effect of changing the flood level of Al-Shuwaija marsh was studied using the geographic information systems, specifically the QGIS program, and the STRM digital elevation model with a spatial analysis accuracy of 28 meters, was used to study the marsh. The hydraulic factors that characterize the marsh and affecting on the flooding such as the ranks of the water channels feeding the marsh and the degree of slope and flat areas in it are studied. The area of immersion water, the mean depth, and the accumulated water volume are calculated for each immersion level, thereby, this study finds the safe immersion level for this marsh was determined.

      Today, the world is living in a time of epidemic diseases that spread unnaturally and infect and kill millions of people worldwide. The COVID-19 virus, which is one of the most well-known epidemic diseases currently spreading, has killed more than six million people as of May 2022. The World Health Organization (WHO) declared the 2019 coronavirus disease (COVID-19) after an outbreak of SARS-CoV-2 infection. COVID-19 is a severe and potentially fatal respiratory disease caused by the SARS-CoV-2 virus, which was first noticed at the end of 2019 in Wuhan city. Artificial intelligence plays a meaningful role in analyzing medical images and giving accurate results that serve healthcare workers, especially X-ray images, which are co

The research aimed to study the role that the media play in shaping the public knowledge of human rights issues among the people of Kirkuk, which will be the focus of the study. The research was conducted by applying a survey panel to a random sample of the city's audience. The research dealt with the theoretical aspect of a theory that relied on the media, and the loans provided by the theory, on the basis of which the research was conducted and the research problem was determined based on a major question: What is the role that the mass media play in developing the knowledge of members of the public on human rights and the relationship between the intensity of view in that, as well as the identification of the effect of two variables G

  This paper deals with proposing new lifting scheme (HYBRID Algorithm) that is capable of preventing images and documents which are fraud through decomposing there in to the real colors value arrays (red, blue and green) to create retrieval keys for its properties and store it in the database and then check the document originality by retrieve the query image or document through the decomposition described above and compare the predicted color values (retrieval keys)  of the query document with those stored in the database. The proposed algorithm has been developed from the two known lifting schemes (Haar and D4) by merging them to find out HYBRID lifting scheme. The validity and accuracy of the proposed algorithm have been ev

     Storing and transferring the images data are raised in recent years due to requisiteness of transmission bandwidth for considerable storage capacity. Data compression method is proposed and applied in an attempt to convert data files into smaller files. The proposed and applied method is based on the Wavelet Difference Reduction (WDR) as considered the most efficient image coding method in recent years. Compression are done for three different Wavelet based Image techniques using WDR process. These techniques are implemented with different types of wavelet codecs. These are Daub2+2,2 Integer Wavelet transform, Daub5/3 integer to integer wavelet transform, and Daub9/7 Wavelet transform with level four. The used mu

In this paper, a hybrid image compression technique is introduced that integrates discrete wavelet transform (DWT) and linear polynomial coding. In addition, the proposed technique improved the midtread quantizer scheme once by utilizing the block based and the selected factor value. The compression system performance showed the superiority in quality and compression ratio compared to traditional polynomial coding techniques.

     The widespread use of images, especially color images and rapid advancement of computer science, have led to an emphasis on securing these images and defending them against intruders. One of the most popular ways to protect images is to use encryption algorithms that convert data in a way that is not recognized by someone other than the intended user. The Advanced Encryption Standard algorithm (AES) is one of the most protected encryption algorithms. However, due to various types of theoretical and practical assaults, like a statistical attack, differential analysis, and brute force attack, its security is under attack.

In this paper, a modified AES coined as (M-AES) is proposed to improve the efficiency