This work is a trial to ensure the absolute security in any quantum cryptography (QC) protocol via building an effective hardware for satisfying the single-photon must requirement by controlling the value of mean photon number. This was approximately achieved by building a driving circuit that provide very short pulses (≈ 10 ns) for laser diode -LD- with output power of (0.7-0.99mW) using the available electronic components in local markets. These short pulses enable getting faint laser pulses that were further attenuated to reach mean photon number equal to 0.08 or less.

The main objective of this work is to introduce and investigate fixed point (F. p) theorems for maps that satisfy contractive conditions in weak partial metric spaces (W.P.M.S), and give some new generalization of the fixed point theorems of Mathews and Heckmann. Our results extend, and unify a multitude of (F. p) theorems and generalize some results in (W.P.M.S). An example is given as an illustration of our results.

In this paper the full stable Banach gamma-algebra modules, fully stable Banach gamma-algebra modules relative to ideal are introduced. Some properties and characterizations of these classes of full stability are studied.

      In this paper, we introduce the concepts of Large-lifting and Large-supplemented modules as a generalization of lifting and supplemented modules.  We also give some results and properties of this new kind of modules.

Abstract In this work we introduce the concept of approximately regular ring as generalizations of regular ring, and the sense of a Z- approximately regular module as generalizations of Z- regular module. We give many result about this concept.

Let R be associative ring with identity and M is a non- zero unitary left module over R. M is called M- hollow if every maximal submodule of M is small submodule of M. In this paper we study the properties of this kind of modules.

Let R be a commutative ring with identity and M be a unitary R- module. We shall say that M is a primary multiplication module if every primary submodule of M is a multiplication submodule of M. Some of the properties of this concept will be investigated. The main results of this paper are, for modules M and N, we have M N and HomR (M, N) are primary multiplications R-modules under certain assumptions.

he concept of small monoform module was introduced by Hadi and Marhun, where a module U is called small monoform if for each non-zero submodule V of U and for every non-zero homomorphism f ∈ Hom R (V, U), implies that ker f is small submodule of V. In this paper the author dualizes this concept; she calls it co-small monoform module. Many fundamental properties of co-small monoform module are given. Partial characterization of co-small monoform module is established. Also, the author dualizes the concept of small quasi-Dedekind modules which given by Hadi and Ghawi. She show that co-small monoform is contained properly in the class of the dual of small quasi-Dedekind modules. Furthermore, some subclasses of co-small monoform are investiga