In this paper, we apply the notion of a bipolar fuzzy n-fold KU-ideal of KU- algebras. We introduce the concept of a bipolar fuzzy n-fold KU-ideal and investigate several properties. Also, we give relations between a bipolar fuzzy n- fold KU-ideal and n-fold KU-ideal. The image and the pre-image of bipolar fuzzy n-fold KU-ideals in KU-algebras are defined and how the image and the pre- image of bipolar fuzzy n-fold KU-ideals in KU-algebras become bipolar fuzzy n- fold KU-ideals are studied. Moreover, the product of bipolar fuzzy n-fold KU- ideals in Cartesian product KU-algebras is given.

In thisˑ paperˑ, we apply the notion ofˑ intuitionisticˑ fuzzyˑ n-fold KU-ideal of KU-algebra. Some types of ideals such as intuitionistic fuzzy KU-ideal, intuitionisticˑ fuzzy closed idealˑ and intuitionistic fuzzy n-fold KU-ideal are studied. Also, the relations between intuitionistic fuzzy n-fold KU-ideal and intuitionistic fuzzy KU-ideal are discussed. Furthermore, aˑ fewˑ results of intuitionisticˑ fuzzyˑ n-ˑfold KU-ideals of a KU-algebra underˑ homomorphismˑ are discussed.

In a connected graph , the distance function between each pair of two vertices from a set vertex  is the shortest distance between them and the vertex degree  denoted by  is the number of edges which are incident to the vertex  The Schultz and modified Schultz polynomials of  are have defined as:

 respectively, where the summations are taken over all unordered pairs of distinct vertices in  and  is the distance between  and  in  The general forms of Schultz and modified Schultz polynomials shall be found and indices of the edge – identification chain and ring – square graphs in the present work.

Markov chains are an application of stochastic models in operation research, helping the analysis and optimization of processes with random events and transitions. The method that will be deployed to obtain the transient solution to a Markov chain problem is an important part of this process. The present paper introduces a novel Ordinary Differential Equation (ODE) approach to solve the Markov chain problem. The probability distribution of a continuous-time Markov chain with an infinitesimal generator at a given time is considered, which is a resulting solution of the Chapman-Kolmogorov differential equation. This study presents a one-step second-derivative method with better accuracy in solving the first-order Initial Value Problem

This study presented an endeavour to integrate the value chain activities with the Balanced Scorecard for a comprehensive evaluation of an organization’s strategic performance. It also demonstrated the connection and the integration of the activities of the value chain with the Balanced Scorecard. The financial measurement was linked with non-financial measurement by integrating these techniques to achieve an appropriate performance that supports all aspects of the organizational performance. Consequently, the research problem in this study emerged, which is due to the concentration of many organizations on the measurement of financial performance. Notably, the latter caused the decline of some organizations from the competitive market. T

It is often needed to have circuits that can display the decimal representation of a binary number and specifically in this paper on a 7-segment display. In this paper a circuit that can display the decimal equivalent of an n-bit binary number is designed and it’s behavior is described using Verilog Hardware Descriptive Language (HDL). This HDL program is then used to configure an FPGA to implement the designed circuit.

The present work involved preparation of new hetro cyclic polyacrylamides (1-9) using reaction of polyacryloyl chloride with 2-aminobenzothiazole which prepeard by thiocyanogen method in the presence of a suitable solvent and amount tri ethyl amine (Et3N) with heating. The structure confirmation of polymers were proved using FT-IR,1H-NMR,C13NMR and UV spectroscopy.Other physical properties including softening and melting points, and solubility of the polymers were also measured.