Let G be a graph with p vertices and q edges and  be an injective function, where k is a positive integer. If the induced edge labeling   defined by for each is a bijection, then the labeling f is called an odd Fibonacci edge irregular labeling of G. A graph which admits an odd Fibonacci edge irregular labeling is called an odd Fibonacci edge irregular graph. The odd Fibonacci edge irregularity strength ofes(G) is the minimum k for which G admits an odd Fibonacci edge irregular labeling. In this paper, the odd Fibonacci edge irregularity strength for some subdivision graphs and graphs obtained from vertex identification is determined.

In this study, the four tests employed for non-linear dependence which is Engle (1982), McLeod &Li (1983), Tsay (1986), and Hinich & Patterson (1995). To test the null hypothesis that the time series is a serially independent and identical distribution process .The linear structure is removed from the data which is represent the sales of State Company for Electrical Industries, through a pre-whitening model, AR (p) model .From The results for tests to the data is not so clear.

This research deals with the dialects of the Arabian Peninsula, which is a group of dialects that belong to one language family. this term that was launched by Dr. Walaa Sadiq Al-Asadi in relation to the site from which the tribes speaking those dialects started, which is the Arabian Peninsula, and the word (dialects) was used  Instead of (languages) considering dialects emanate from collective language, which is what is called the mother tongue of those dialects

In the present paper, chitosan Schiff base has been synthesized from chitosan’s reaction with the salicyldehyde. The AuNPs was manufacture by extract of onion peels as a reducing agent. The Au NPs that have been prepared were characterized through the UV-vis spectroscopy, XRD analyses and SEM microscopy. The polymer blends of the chitosan Schiff base / PVP has been prepared through using the approach of solution casting. Chitosan Schiff base / PVP Au nano-composites was prepared. Nano composites and polymer blends have been characterized by FTIR which confirm the formation of Schiff base by revealing a new band of absorption at 1651cm^-1 as a result of the (C=N) imine group. SEM, DSC and TGA confirms the thermal stability of

In the present paper, chitosan Schiff base has been synthesized from chitosan’s reaction with the salicyldehyde. The AuNPs was manufacture by extract of onion peels as a reducing agent. The Au NPs that have been prepared were characterized through the UV-vis spectroscopy, XRD analyses and SEM microscopy. The polymer blends of the chitosan Schiff base / PVP has been prepared through using the approach of solution casting. Chitosan Schiff base / PVP Au nano-composites was prepared. Nano composites and polymer blends have been characterized by FTIR which confirm the formation of Schiff base by revealing a new band of absorption at 1651cm-1 as a result of the (C=N) imine group. SEM, DSC and TGA confirms the thermal stability of the pr

         In this paper, developed Jungck contractive mappings into fuzzy Jungck contractive and proved  fuzzy fixed point for some types of generalize fuzzy Jungck contractive mappings.

The theory of probabilistic programming  may be conceived in several different ways. As a method of programming it analyses the implications of probabilistic variations in the parameter space of linear or nonlinear programming model. The generating mechanism of such probabilistic variations in the economic models may be due to incomplete information about changes in demand, pro­duction and technology, specification errors about the econometric relations presumed for different economic agents, uncertainty of various sorts and the consequences of imperfect aggregation or disaggregating of economic variables. In this Research we discuss the probabilistic programming problem when the coefficient b_i is random variable

   Let M is a Г-ring. In this paper the concept of orthogonal symmetric higher bi-derivations on semiprime Г-ring is presented and studied and the relations of two symmetric higher bi-derivations on Г-ring are introduced.

The aim of this research is to study some types of fibrewise fuzzy topological spaces. The six major goals are explored in this thesis. The very first goal, introduce and study the notions types of fibrewise topological spaces, namely fibrewise fuzzy j-topological spaces, Also, we introduce the concepts of fibrewise j-closed fuzzy topological spaces, fibrewise j-open fuzzy topological spaces, fibrewise locally sliceable fuzzy j-topological spaces and fibrewise locally sectionable fuzzy j-topological spaces. Furthermore, we state and prove several Theorems concerning these concepts, where j={δ,θ,α,p,s,b,β} The second goal is to introduce weak and strong forms of fibrewise fuzzy ω-topological spaces, namely the fibrewise fuz

In this work, two different structures are proposed which is fuzzy real normed space (FRNS) and fuzzy real Pre-Hilbert space (FRPHS). The basic concept of fuzzy norm on a real linear space is first presented to construct  space, which is a FRNS with some modification of the definition introduced by G. Rano and T. Bag. The structure of fuzzy real Pre-Hilbert space (FRPHS) is then presented which is based on the structure of FRNS. Then, some of the properties and related concepts for the suggested space FRN such as -neighborhood, closure of the set  named , the necessary condition for separable, fuzzy linear manifold (FLM) are discussed. The definition for a fuzzy seminorm on  is also introduced with the prove that a fuzzy seminorm on