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.

In this paper, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined; also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin’s maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem.

The purpose of this paper is to solve the stochastic demand for the unbalanced transport problem using heuristic algorithms to obtain the optimum solution, by minimizing the costs of transporting the gasoline product for the Oil Products Distribution Company of the Iraqi Ministry of Oil. The most important conclusions that were reached are the results prove the possibility of solving the random transportation problem when the demand is uncertain by the stochastic programming model. The most obvious finding to emerge from this work is that the genetic algorithm was able to address the problems of unbalanced transport, And the possibility of applying the model approved by the oil products distribution company in the Iraqi Ministry of Oil to m

      Many neuroscience applications, including understanding the evolution of the brain, rely on neural cell instance segmentation, which seeks to integrate the identification and segmentation of neuronal cells in microscopic imagery. However, the task is complicated by cell adhesion, deformation, vague cell outlines, low-contrast cell protrusion structures, and background imperfections. On the other hand, existing segmentation approaches frequently produce inaccurate findings. As a result, an effective strategy for using the residual network with attention to segment cells is suggested in this paper. The segmentation mask of neural cells may be accurately predicted. This method is built on U-net, with EfficientNet serving as the e

Many fuzzy clustering are based on within-cluster scatter with a compactness measure , but in this paper explaining new fuzzy clustering method which depend on within-cluster scatter with a compactness measure and between-cluster scatter with a separation measure called the fuzzy compactness and separation (FCS). The fuzzy linear discriminant analysis (FLDA) based on within-cluster scatter matrix and between-cluster scatter matrix . Then two fuzzy scattering matrices in the objective function assure the compactness between data elements and cluster centers .To test the optimal number of clusters using validation clustering method is discuss .After that an illustrate example are applied.

Praise be to God, who is satisfied with Islam as our religion, “He opened a clear conquest for us,” and whoever works with us through the Shari’ah works and protects us. And that our master and Mawlana Muhammad His servant and Messenger is a prophet who has been merciful and compassionate. "
And after:
The occupation of Iraq and the accompanying bone events, and the following severe obstacles, resulted in a set of problems that require legitimate stances, and satisfactory answers, remove confusion and delusion, amid the clash of opinions and contradictions of jurisprudence. Work and application.
Among the difficult problems that surfaced in light of the new political developments on the land of Iraq: (the ruling on dealing

  Osteoporosis is related to the loss of bone mass that occurs as part of the natural process of aging and in menopausal women.           The aim of this study is to evaluate the levels of interleukin-35 in menopausal women with osteoporosis, that may be used as an early predicted marker of osteoblastic and osteoclastic activity in osteoporosis patients in relation with other diagnostic parameters.           Fasting blood samples were obtained from forty Iraqi menopausal women with mean age of (61.06±6.59)years who were newly diagnosed of osteoporosis by physicians at Baghdad Teaching Hospital as patients group(G1). In addition to , twenty two healthy women were included in the st

Background: Otitis media with effusion is characterized by accumulation of fluid in the middle ear in absence of acute inflammation and  it is the most common cause of  acquired hearing loss in children, and may  negatively affect language development failure of medical treatment of middle ear effusion frequently require myringotomy and tympanostomy tube insertion.

Objectives: To determine tympanostomy tube complications of tube in children with chronic otitis media with effusion who were treated with Shah Grommet tube insertion.

Methods: The Medical records of 162 ears of 87 children (52 male and 35 female) were reviewed respectively, the patients ages wer

BACKGROUND: Preeclampsia (PE) is a possible etiology of obstetrical and neonatal complications which are increased in resource-limited settings and developing countries. AIM: We aimed to find out the prevalence of PE in Iraqi ladies and specific outcomes, including gestational weight gain (GWG), cesarean section (CS), preterm delivery (PD), and low birth weight (LBW). METHODS: All singleton pregnant women visiting our tertiary center for delivery were involved over 3 years. PE women were compared with non-PE ladies. Complete history and examination were done during pregnancy and after delivery by the attending obstetrician and neonatologist with full documentation in medical records. RESULTS: PE prevalence was 4.79

     In today's world, digital image storage and transmission play an essential role,where images are mainly involved in data transfer. Digital images usually take large storage space and bandwidth for transmission, so image compression is important in data communication. This paper discusses a unique and novel lossy image compression approach. Exactly 50% of image pixels are encoded, and other 50% pixels are excluded. The method uses a block approach. Pixels of the block are transformed with a novel transform. Pixel nibbles are mapped as a single bit in a transform table generating more zeros, which helps achieve compression. Later, inverse transform is applied in reconstruction, and a single bit value from the table is rem