In this work, we consider a modification of the Lotka-Volterra food chain model of three species, each of them is growing logistically. We found that the model has eight equilibrium points, four of them always exist, while the rest exist under certain conditions. In terms of stability, we found that the system has five unstable equilibrium points, while the rest points are locally asymptotically stable under certain satisfying conditions. Finally, we provide an example to support the theoretical results.

Making the data secure is more and more concerned in the communication era. This research is an attempt to make a more secured information message by using both encryption and steganography. The encryption phase is done with dynamic DNA complementary rules while DNA addition rules are done with secret key where both are based on the canny edge detection point of the cover image. The hiding phase is done after dividing the cover image into 8 blocks, the blocks that are used for hiding selected in reverse order exception the edge points. The experiments result shows that the method is reliable with high value in PSNR

This paper deals with constructing a model of fuzzy linear programming with application on fuels product of Dura- refinery , which consist of seven products that have direct effect ondaily consumption . After Building the model which consist of objective function represents the selling prices ofthe products and fuzzy productions constraints and fuzzy demand constraints addition to production requirements constraints , we used program of ( WIN QSB )  to find the optimal solution

In this paper, new concepts which are called: left derivations and generalized left derivations in nearrings have been defined. Furthermore, the commutativity of the 3-prime near-ring which involves some
algebraic identities on generalized left derivation has been studied.

The continuous growth in technology and technological devices has led to the development of machines to help ease various human-related activities. For instance, irrespective of the importance of information on the Steam platform, buyers or players still get little information related to the application. This is not encouraging despite the importance of information in this current globalization era. Therefore, it is necessary to develop an attractive and interactive application that allows users to ask questions and get answers, such as a chatbot, which can be implemented on Discord social media. Artificial Intelligence is a technique that allows machines to think and be able to make their own decisions. This research showed that the dis

In this paper ,we introduce hollow modules with respect to an arbitrary submodule .Let M be a non-zero module and T be a submodule of M .We say that M is aT-hollow module if every proper submodule K of M such that T ⊈ K is a T-small submodule of M .We investigate the basic properties of a T-hollow module

In previous our research, the concepts of visible submodules and fully visible modules were introduced, and then these two concepts were fuzzified to fuzzy visible submodules and fully fuzzy. The main goal of this paper is to study the relationships between fully fuzzy visible modules and some types of fuzzy modules such as semiprime, prime, quasi, divisible, F-regular, quasi injective, and duo fuzzy modules, where under certain conditions it has been proven that each fully fuzzy visible module is fuzzy duo. In addition, there are many various properties and important results obtained through this research, which have been illustrated. Also, fuzzy Artinian modules and fuzzy fully stable modules have been introduced, and we study the rel

In this paper, simulation studies and applications of the New Weibull-Inverse Lomax (NWIL) distribution were presented. In the simulation studies, different sample sizes ranging from 30, 50, 100, 200, 300, to 500 were considered. Also, 1,000 replications were considered for the experiment. NWIL is a fat tail distribution. Higher moments are not easily derived except with some approximations. However, the estimates have higher precisions with low variances. Finally, the usefulness of the NWIL distribution was illustrated by fitting two data  sets

Contemporary life is racing against time in its temptations and variables, and it has become shaped and changed in an amazing way in its various aspects and fields. This was facilitated by intellectual and scientific communication between civilizations, and the rapid progression in successive inventions and discoveries in the fields of science and arts of knowledge. This contributed to a great economic and commercial renaissance. Then, these economic developments entered the world into a very strong competition, which forced producers to calculate all production costs, to reach the highest profits by reducing the price of the produced commodity on the one hand, and achieving quality in appearance (especially) on the other hand. Since the ma