علاء محمد رضا عبد الحسن دعيبل

Let 𝐺 = (𝑉,𝐸) be a graph with 𝑉 = 𝑉 (𝐺) and 𝐸 = 𝐸(𝐺). A function 𝑓∶ 𝑉 → {0,1,2} is said to be an Italian dominating function on a graph 𝐺 if every vertex 𝑢 with 𝑓 (𝑢)=0 is adjacent to at least one vertex 𝑣 with 𝑓 (𝑣)=2 or is adjacent to at least two vertices 𝑥,𝑦 with 𝑓 (𝑥) = 𝑓 (𝑦) = 1. The value 𝑤(𝑓 ) = Σ𝑓 (𝑣)𝑣∈𝑉 denotes the weight of an Italian dominating function. The minimum weight taken over all Italian dominating functions of 𝐺 is called Italian domination number and denoted by 𝛾𝐼(𝐺). Two parameters related to Italian dominating function (IDF) are restrained Italian (RIDF) and total restrained (TRDF) dominating functions 𝑓 , for which the set of vertices 𝑣 with 𝑓 (𝑣) = 0, and simultaneously the set of vertices 𝑣 with 𝑓 (𝑣) > 0 and the set of vertices 𝑣 with 𝑓 (𝑣)= 0 induce subgraphs with no isolated vertex respectively. The central graph 𝐶(𝐺) of a graph 𝐺 is the graph obtained by subdividing each edge of 𝐺 exactly once and joining all the non-adjacent vertices of 𝐺. In this work, we initiate the study of restrained (total restrained) Italian domination number of the central of any graph 𝐺. For a family of standard graphs 𝐺, we obtain the precise value of restrained (total restrained) Italian domination number for 𝐶(𝐺), indeed for any graph G, the sharp bounds are provided for 𝐶(𝐺), and for 𝐺 corona of 𝐾1 , 𝐺∘𝐾1 we establish the precise value of these parameters for 𝐶(𝐺∘𝐾1).

Robots that operate in real-world settings must be able to recognize, model, and infer the semantic features of things. Existing frameworks for knowledge reasoning are only able to describe the binary relationships between the semantic qualities of an item and its class label; they are unable to reason about the attributes of objects that are identified by various perception algorithms and based on a variety of sensory modalities. We provide an n-ary representation that describes intricate, interconnected object attributes in order to bridge the gap between multimodal perception and knowledge reasoning. In this work, we present an algebraic properties of operations on n-ary relation soft set, which is more functional to make practical and theoretical ideas or studies in the soft set theory. We center around the fundamental algebraic properties of operations on the n-ary relation soft set and study some propositions of these algebraic properties. This new properties are advantageous and contributes in some scientific applications.

The aim of this article is to associate a tritopological space with a locally finite graph, and induce a new type of topology from three well-known topologies on the same locally finite graph. These are the three tritopologies proposed recently to associate topological spaces with undirected graphs, the first (Independent Topology), the second is (Non-Incidence Topology) and the third is (Graphic Topology). Then some results and properties of these tritopological spaces and new induced topologies were investigated. Giving a fundamental step toward studying some properties of locally finite graphs by their corresponding tritopological spaces is our motivation.

The main object of this paper is to introduce and study some triple sequence spaces are defined by a non-negative six-dimensional matrix and a double modulus function (X, Y) = (x u,v,w,i,m,n , y u,v,w,i,m,n ) in real numbers ℝ and complex numbers ℂ. In addition, it is also possible to obtain and prove some merging relations. And using those operations conducted in the research to find some important properties such as solidity, symmetry, etc. Some basic equations for convergence spaces can be used to find some differential and integral equations with which. And using those equations to find the transformation of one-dimensional matrices into six-dimensional matrices by using some special software to find solutions of some differential equations affiliated with the three-spaces defined by the multiplicative modulus function and using them in some mathematical fields, including real and complex ones.

Spontaneous recognition of human faces is a challenging problem that has install important concern from signal processing researchers in Last years. This is owing to its many uses in various fields, including security and forensic analysis. Notwithstanding this interest, face recognition is yet one of the most challenging troubles. Up to this time, no way gives a good solution to all attitudes. In this paper we present a neoteric mathematical technicality for face recognition. which we call, (ITSM), is Accredit on our lately disseminated efficient information-theoretic-statistical equation (ITSM), which Merge three mathematically balanced equations. The first one is entropic equation (EE), the second one is histogram equation (HE), and the third one is the standard statistic (SSIM). (ITSM) Tested against versus (SSIM) and (ITSSIM) beneath Gaussian noise, so we got good results even beneath a large scale of PSNR. The face recognition with (ITSM) certified on both above measures of a test image and a database images. We performed the performance evaluation with (MATLAB) using part of the Famous (AT&T) gray Image Database that made up of (49) face images, from which we chose seven person and for each one we chose seven Perspectives (poses) with different facial emotions. The Target of this paper is to present an efficient technicality for face recognition that may work in real-time milieu. Through the implementation of our information, facial recognition has been proven with a method (ITSM) Hybrid (information - theoretic-statistical) that surpasses the known statistical technicality of face recognition (SSIM) and a technicality based on information theory known as (ISSIM).

Several methods of image similarity were introduced to handle different forms of distortions of the image. Most of these techniques are based on statistics, other techniques are information-theoretical that are more modern and more effective than mathematical. in this paper, we present a different than its Common technique, a hybrid face image similarity measure by merging statistic and information theory, which is called in this paper as (ITSM), The proposed method (ITSM) Joins three mathematically balanced equations. The first we have newly created in this paper, entropic equation (EE) based on standard information-theoretic measures like (Shannon entropy, joint entropy). The second also newly created, histogram equation (HE) based on (image histogram and joint histogram). The third one is the standard statistic (SSIM). The (ITSM) was tested in Gaussian noise versus (SSIM) and Histogram-Entropic Scale (ITSSIM), where good results were obtained even under a large range of PSNRs. Simulation tests using the MATLAB images, (AT&T and FEI Brazilian face image) databases indicate that the Suggested hybrid technique outperforms the (SSIM) and (ITSSIM) techniques by being able to detect resemblance in faces under very low PSNR.