<p>In this paper, we prove there exists a coupled fixed point for a set- valued contraction mapping defined on X× X , where X is incomplete ordered G-metric. Also, we prove the existence of a unique fixed point for single valued mapping with respect to implicit condition defined on a complete G- metric.</p>

The Detour distance is one of the most common distance types used in chemistry and computer networks today. Therefore, in this paper, the detour polynomials and detour indices of vertices identified of n-graphs which are connected to themselves and separated from each other with respect to the vertices for n≥3 will be obtained. Also, polynomials detour and detour indices will be found for another graphs which have important applications in Chemistry.

          The present paper studies the generalized Φ-  recurrent of Kenmotsu type manifolds. This is done to determine the components of the covariant derivative of the Riemannian curvature tensor. Moreover, the conditions which make Kenmotsu type manifolds to be locally symmetric or generalized Φ- recurrent have been established. It is also concluded that the locally symmetric of Kenmotsu type manifolds are generalized recurrent under suitable condition and vice versa. Furthermore, the study establishes the relationship between the Einstein manifolds and locally symmetric of Kenmotsu type manifolds.

Non-additive measures and corresponding integrals originally have been introduced by Choquet in 1953 (1) and independently defined by Sugeno in 1974 (2) in order to extend the classical measure by replacing the additivity property to non-additive property. An important feature of non –additive measures and fuzzy integrals is that they can represent the importance of individual information sources and interactions among them. There are many applications of non-additive measures and fuzzy integrals such as image processing, multi-criteria decision making, information fusion, classification, and pattern recognition. This paper presents a mathematical model for discussing an application of non-additive measures and corresp

A novel design and implementation of a cognitive methodology for the on-line auto-tuning robust PID controller in a real heating system is presented in this paper. The aim of the proposed work is to construct a cognitive control methodology that gives optimal control signal to the heating system, which achieve the following objectives: fast and precise search efficiency in finding the on- line optimal PID controller parameters in order to find the optimal output temperature response for the heating system. The cognitive methodology (CM) consists of three engines: breeding engine based Routh-Hurwitz criterion stability, search engine based particle
swarm optimization (PSO) and aggregation knowledge engine based cultural algorithm (CA)

This project presents an enhanced Iraqi vehicle plate identification system, incorporating digital processing technologies and the XOR Auto-Associative Memory advanced associative memory algorithm, towards a fast and efficient performance under diverse conditions of imagery. The system consists of three major stages: identification of the panel area, or localization, using edge transformations and morphological operations; symbol segmentation, or segmentation, based on horizontal and vertical projections for the exact extraction of numbers and letters; and finally, recognition use of XOR operations and a binary distance criterion known as Hamming Distance. The model was tested on 420 images of panels in different scenarios of lighting

A new class of higher derivatives  for harmonic univalent functions defined by a generalized fractional integral operator inside an open unit disk E is the aim of this paper.