Let R be an associative ring with identity and M be unital non zero R-module. A
submodule N of a module M is called a δ-small submodule of M (briefly N << M )if
N+X=M for any proper submodule X of M with M/X singular, we have
X=M .
In this work,we study the modules which satisfies the ascending chain condition
(a. c. c.) and descending chain condition (d. c. c.) on this kind of submodules .Then
we generalize this conditions into the rings , in the last section we get same results
on δ- supplement submodules and we discuss some of these results on this types of
submodules.

There is no access to basic sanitation for half the world's population, leading to Socioeconomic issues, such as scarcity of drinking water and the spread of diseases. In this way, it is of vital importance to develop water management technologies relevant to the target population. In addition, in the separation form of water treatment, the compound often used as a coagulant in water treatment is aluminum sulfate, which provides good results for raw water turbidity and color removal. Studies show, however, that its deposition in the human body, even Alzheimer's disease, can cause serious harm to health and disease development. The study aims to improve the coagulation/flocculation stage related to the amount of flakes, i

This paper describes a microcontroller-based function generator system. By the function generator sine wave, square wave, quasi-square wave, saw-tooth and triangular waveforms are generated over a wide frequency range according to user requirements. By utilizing processing capabilities of the microcontroller the hardware is minimized exceedingly. The output waveform shapes are digitally-controlled to achieve the required wave shape. The single chip microcomputer of waveform generation equipment offers the possibility of improvements in manufacture reliability, maintenance and servicing and increased control flexibility. The system is built and tested. The results of test were satisfactory and appreciated by test engineers at different ce

The study aimed to assess the frequency of invasive fungal infection in patients with respiratory diseases by conventional and molecular methods. This study included 117 Broncho alveolar lavage (BAL) samples were collected from patients with respiratory disease (79 male and 38 female) with ages ranged between (20-80) years, who attended Medicine Baghdad Teaching hospital and AL-Emamain AL-Khadhymian Medical City, during the period from September 2019 to April 2020. The results in PCR versus culture methods in this study showed that out of 117 samples of fungal infections 30(25.6 %) were detected by culture method, while the 24(20.5%) samples were detected by PCR technique, the most commonly diagnosed pathogenic fungi is Candida spp.

Background: The change in the concepts of cavity preparation and the development of reliable adhesive materials lead to the development of alternative methods of caries removal. Chemo-mechanical caries removal (CMCR) involves the chemical softening of carious dentin, followed by its removal with manual excavation. The present study was conducted to evaluate clinically the efficiency of caries removal using a new chemo-mechanical agent (Papacarie) compared to the conventional drilling method in reduction of total bacterial count. Material and methods: The study is a split mouth design. The sample composes from sixty mandibular deciduous molars teeth in thirty children, between six to nine years of age with bilateral class I deep occlusal car

Individual cannot live alone due to to his need for others to facilitate His supplies for living, thus social affiliation is considered one of the most important psychological, social needs in individuals life through his willing to affiliate to others whether they were friends ,family, colleague , or even home to reach some degree of  psychological stability.

       Affiliation is a tool to search for Satiate through living with group from the same type or comply for group or to be compatible with them or even to be adherent and accept what the group agreed about of criterion.

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The current study is the identification and isolation dermatophyte species in clinical isolates by both Sabouraud’s Dextrose Agar (SDA) and on Dermatophyte Test Medium (DTM). Clinical specimens of hair, nails and skin scales were collected from patients with dermatophytosis and submitted to direct microscopic examination after immersion in 20% of potassium hydroxide solution. The clinical specimens were cultured on SDA containing chloramphenicol and cycloheximide, and on DTM. Tinea corporis showed the highest prevalent dermatophyte infection among patients (26.7%), followed by Tinea pedis (23.3%), whereas Tinea manuum exhibited the lowest fungal infection (6.7 %). Rural areas revealed the highest prevalence of dermatophyte in

The present work included study of the effects of weather conditions such as solar radiation and  ambient temperature on solar panels (monocrystalline 30 Watts) via proposed mathematical model, MATLAB_Simulation was used by scripts file to create a special code to solve the mathematical model , The latter is single –diode model (Five parameter) ,Where the effect of ambient temperature and solar radiation on the output of the solar panel was studied, the Newton Raphson method was used to find the  output current of the solar panel and plot P-V ,I-V curves, the performance of the PV was determined at Standard Test Condition (STC) (1000W/m2)and a comparison between theoretical and experimental results were done .The best efficiency