In this paper we introduce the notions of t-stable extending and strongly t-stable extending modules. We investigate properties and characterizations of each of these concepts. It is shown that a direct sum of t-stable extending modules is t-stable extending while with certain conditions a direct sum of strongly t-stable extending is strongly t-stable extending. Also, it is proved that under certain condition, a stable submodule of t-stable extending (strongly t-stable extending) inherits the property.

This paper proposes a novel method for generating True Random Numbers (TRNs) using electromechanical switches. The proposed generator is implemented using an FPGA board. The system utilizes the phenomenon of electromechanical switch bounce to produce a randomly fluctuated signal that is used to trigger a counter to generate a binary random number. Compared to other true random number generation methods, the proposed approach features a high degree of randomness using a simple circuit that can be easily built using off-the-shelf components. The proposed system is implemented using a commercial relay circuit connected to an FPGA board that is used to process and record the generated random sequences. Applying statistical testing on the exp

     Let  be an R-module, and let  be a submodule of . A submodule  is called -Small submodule () if for every submodule  of  such that  implies that . In our work we give the definition of -coclosed submodule and -hollow-lifiting modules with many properties.

In this paper, a new class of harmonic univalent functions was defined by the differential operator. We obtained some geometric properties, such as the coefficient estimates, convex combination, extreme points, and convolution (Hadamard product), which are required

Let  be a ring with identity and  be a submodule of a left - module . A submodule  of  is called - small in  denoted by , in case for any submodule  of ,  implies .  Submodule  of  is called semi -T- small in , denoted by , provided for submodule  of ,  implies that . We studied this concept which is a generalization of the small submodules and obtained some related results

Fiber-to-the-Home (FTTH) has long been recognized as a technology that provides future proof bandwidth [1], but has generally been too expensive to implement on a wide scale. However, reductions in the cost of electro-optic components and improvements in the handling of fiber optics now make FTTH a cost effective solution in many situations. The transition to FTTH in the access network is also a benefit for both consumers and service providers because it opens up the near limitless capacity of the core long-haul network to the local user. In this paper individual passive optical components, transceivers, and fibers has been put together to form a complete FTTH network. Then the implementation of the under construction Baghdad/Al

We introduce the notion of t-polyform modules. The class of t- polyform modules contains the class of polyform modules and contains the class of t-essential quasi-Dedekind.

     Many characterizations of t-polyform modules are given. Also many connections between these class of modules and other types of modules are introduced.

In this research want to make analysis for some indicators and it's classifications that related with the teaching process and the            scientific level for graduate studies in the university by using analysis of variance for ranked data for repeated measurements instead of the ordinary analysis of variance . We reach many conclusions  for the                         

important classifications for each indicator that has affected on   the teaching process.         &nb

Internal Music is considered as a basis to form music melody that sends rapture and
ecstasy within ones selves since it occurs directly on ears ( hearing) and since it tightens the
meaning to make it penetrating into Heart. It is rhythmic organization occurred inside the text
due to movements of internal sounds since rhythm heavily depends on language and
pronunciation. Repetition adds music melody to the poetic text since it increases music in
poetry. The sounds that reoccurred either be letters or words are no more than confirmation.
Thus , repetition is artistic phenomena most poets resorted to as to diverse his subjects and
metaphors he depicts in his poetry. The repetition has achieved artistic aesthetics , mean

In this paper we introduce a new class of operators on Hilbert space. We
call the operators in this class, n,m- powers operators. We study this class
of operators and give some of their basic properties.