In this communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions and Binet formulas for these hybrid quaternions and investigating some properties among them.

The problem of poverty and deprivation constitute a humanitarian tragedy and its continuation may threaten the political achievements reached by the State. Iraq, in particular, and although he is one of the very rich countries due to availability of huge economic wealth, poverty indicators are still high. In addition, the main factor in the decline in the standard of living due to the weakness of the government's performance in the delivery of public services of water, electricity and sanitation. Thus, the guide for human development has been addressed which express the achievements that the state can be achieved both on a physical level or on the human level, so in order to put appropriate strategies and policies aimed at elimin

Objective. Glass-ionomer and resin-modified glass-ionomer cements are versatile materials with the ability to form a direct bond with tooth tissues. The aim of this study was to formulate a novel class of dental bio-interactive restorative material (pRMGIC) based on resin-modified glass-ionomer cements via the inclusion of an organophosphorus monomer, ethylene glycol methacrylate phosphate, with a potential to improve the mechanical properties and also function as a reparative restorative material. Methods. pRMGIC was formulated with modification of the resin phase by forming mixes of ethylene glycol methacrylate phosphate (EGMP; 0–40%wt) and 2-hydroxyethyl methacrylate monomer into the liquid phase of a RMGIC (Fuji II LC, GC Corp.).

In this research, has been to building a multi objective Stochastic Aggregate Production Planning model for General al Mansour company Data with Stochastic  demand under changing of market and uncertainty environment in aim to draw strong production plans.  The analysis to derive insights on management issues regular and extra labour costs and the costs of maintaining inventories and good policy choice under the influence medium and optimistic adoption of the model of random has adoption form and had adopted two objective functions total cost function (the core) and income and function for a random template priority compared with fixed forms with objective function and the results showed that the model of two phases wit

In this paper, we investigate and characterize the effects of multi-channel and rendezvous protocols on the connectivity of dynamic spectrum access networks using percolation theory. In particular, we focus on the scenario where the secondary nodes have plenty of vacant channels to choose from a phenomenon which we define as channel abundance. To cope with the existence of multi-channel, we use two types of rendezvous protocols: naive ones which do not guarantee a common channel and advanced ones which do. We show that, with more channel abundance, even with the use of either type of rendezvous protocols, it becomes difficult for two nodes to agree on a common channel, thereby, potentially remaining invisible to each other. We model this in