The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

This research entitled: "Artistic processing of Emotional Scenes in the Narrative Film" deals with how to process and embody those emotional scenes. As there are certain filmic elements that play an effective role in deepening the viewer's sense of the importance of those scenes, and that their presence in the film is necessary and inevitable, and cannot be dispensed because it forms an interconnected connection with the rest of the film's scenes, in addition to its dramatic and aesthetic value in the film in crystallizing the viewer's feelings and integrating him/her into the scene.
The research was divided into four chapters, the first chapter includes: the methodological framework, which represented the research problem, and brin

The killing of Imam Hussein (AS) and his family and his companions is a big tragedy that has sustained Islam and Muslims has remained generations Islamic considers the death of Hussein (AS) of the major calamities and pays homage to the memory of grief and mourning . The taking Shiite poets their active role in the perpetuation of this painful anniversary taken by the Shiites that way to stimulate and stir up emotions against the killers of Ahl al-Bayt ( peace be upon them ) has not missed poets of Andalusia and Shiites from this Wave Shiite overwhelming Vahioa anniversary and Ozvoha best recruit barely era of eras Andalusian literature but was Hussein certificate ( AS) on the tenth of Muharram day Consolation year held the celebrations

This paper aims to study the rate of star formation (SFR) in luminous infrared galaxies at different wavelengths using distance measurement techniques (dl, dm) and to know which methods are the most accurate to determine the rate of star formation as we present through this research the results of the statistical analysis (descriptive statistics) for a sample of luminous infrared galaxies. The data used in this research were collected from the NASA Extragalactic Database (NED) and HYPERLEDA, then used to calculate the star formation rate and indicate the accuracy of the distance methods used (dl, dm). Two methods were tested on Hα, OII, FIR, radio continuum at 1.4 GHz, FUV, NUV, and total (FUV + FIR). The results showed that the dl

This study illustrates the impact of non-thermal plasma (Cold Atmospheric Plasma CAP) on the lipids blood, the study in vivo. The lipids are (cholesterol, HDL-Cholesterol, LDL-Cholesterol and triglyceride) are tested. (FE-DBD) scheme of probe diameter 4cm is used for this purpose, and the output voltage ranged from (0-20) kV with variable frequency (0-30) kHz. The effect of non-thermal atmospheric plasma on lipids were studied with different exposure durations (20,30) sec. As a result, the longer plasma exposure duration decreases more lipids in blood.

The effect ©? acid and alkility for the dichromate solution and the thicknness of gelatin layer on the effecincy of the film , also the time period between the recording and the reconstraction processes . the last effecincy was 90% for PH=5.6 and 95% for d=110 ?? . the highe effeciny for time period was 82% for 48 h .