Table of contents

Many papers were introduced about the best approximation. But little introduced for simultaneous best approximation for L_p Simultaneous approximation. Here we introduce some results for L_p, p≥1, simultaneous approximation.

In this section, we will explain some concepts such as (${\mathscr{C}}$-local function, ${\mathscr{C}}$-closure operator, ${\mathscr{C}}$-local function, ${{\mathscr{C}}}^{* }$-topology and compatible of center ideal space) with clarification of relationships.

The purpose of this paper is to present a formal definition of the computational fuzzy topology is shown which is based on the fuzzy ω-interior operator and fuzzy ω-closure operators. In spatial object modeling the fUzzy ω-interior, fUzzy ω-exterior, fuzzy ω-closure and fuzzy ω-boundary are computed based on computational fuzzy topology and we applied this studied and we determined the fuzzy ω-interior, fuzzy ω-exterior, fuzzy ω-closure and fuzzy ω-boundary of flood affected areas in Iraq and we obtained several properties.

In this paper, we complete an early result by R. Khosravi and M. Roueentan on the hollow act and obtained new properties and characterizations for this notion continues the account of hollow act for commutative monoids begun on 2019. This notion (hollow acts) represents a dual notion to the uniform acts which were submit by M. Roueentan and M. Sedaghatjoo on 2017. An S-act Ms is referred to as hollow act if every subact N_s of M_s is small where a subact Ns is called small (or superfluous) in M_s if for every subact H_s of M_S, N_S∪H_S=M_S implies H_s=M_s. Equally, we reformulate this definition in another words as follows: an S-act M_s is referred to as hollow if whenever N₁,N₂ are subacts of M_s and N₁ ∪N₂ = M_s implies either N₁=M_s or N₂= M_s. Conditions under which subacts are inheriting the property of the Hollow act have been examined. As well as the condition on the quotient subact to be Hollow act was studied. Other properties of the small subact differ from those properties which were early studied by the author are investigated. In the interests of simplicity, the relationship between hollow acts and cyclic act is considered. As a consequence, conditions to coincide those classes are shown. Ultimately, the notion of the Hollow act was used to study when the endomorphism monoid will be local.

For Americans who wish to adopt children from other countries, international adoption visas are issued to the child for entrance into the United States. With the Laws and regulations are changing so often, the number of international adoptions fluctuating with these changes. We are interested in forecasting future visa values from prior visa value data. Our results support that it is possible to predict future international adoption visa numbers but for only a few years into the future due to the laws and regulations changing frequently.

In this paper we introduced a new family of L. P. O. ${\overline {\cal B} _{\dot m,\widehat r}}$ which represent a generalization of Bernstein oper. for a continuous function on the interval [0,1] . Our goal is to study the approximation properties of this sequence and study the uniformly convergence of it on some continuous functions on a compact set [0,1]. We find a rate of this convergence using a modulus of continuity. Finally we establish a formula of a Voronoviskaja-type asymptotic formula on ${\overline {\cal B} _{\dot m,\widehat r}}$.

The Julia set is one of the most remarkable and exciting fields of dynamic mathematics Because it contains very beautiful graphics.

Through this study we will highlight how the filled Julia set is computed. It is worth noting that there is an integrative work between computers and mathematical calculations to get great results to complete Julia Set filling process

Previous research has dealt with the topic of topological graph in several aspects and has studied the set of vertices or set of edges as a sub basis for topological space. The topic of domination has received the attention of many researchers in the recent period, because has many applications in the field of computers and networks. The main purpose of this paper is join between topological space and minimal dominating sets of a graph G, By using all minimal dominating sets (MDS) as open set of topology on V (G) . this paper discussed T₂ – MDS (hausdorff property) of path P_n with n ≥ 4.

In this paper the fundamental concept of repeated linear interpolation and its possible applications in computer-aided geometric design, and start considering basic constructive methods for curves and surfaces. We discuss here a repeated linear interpolation method that we commonly find in computer graphics and geometric modelling. Repeated linear Interpolation means to calculate a polynomial by using several points. For a given sequence of points, this means to estimate a curve that passes through every single point. The purpose of this paper is to construct a polynomial of degree less than or equal to n, by using repeated linear Interpolation.

The aim of this paper is to establish a new family of Baskakov – type operators represented by summation type generalized Baskakov operators. Primarily, we discuss the properties of this sequences of L. P. O.. Further we view some approximation properties which lead us to establish a Voronovskaja theorem on this operators. Also, we study the rate of convergence when we show this new family preserve properties of modulus of continuity on a continuous function.

We study the Sobolev inqualities of real functions defined on graphs, when 0 < p < 1. These spaces are important than that the space of continuous functions.

In this paper we define the canonical embedding and study the existence of S_p(G) which far from ${\displaystyle l}_{p}^{m}$ when 0 < p < 1. Also we estimate the subspace of S_p(G) isomorphic to ${\displaystyle l}_{p}^{d}$ by Banach-Mazur distance of the corresponding dimension for 0 < p < 1.

In this paper we introduced and study some types of fuzzy connected spaces like (Ω- connected space, α – Ω-connected space, feebly-connected space, α-connected space, β- connected space, Sp-connected space, a-connected space) and the relationships between them and fuzzy δ-connected space in fuzzy topological space on fuzzy set. And We give counter examples if they are invalid And introduce Some theorems are included about this object.

This research concentrates on the study of SA / TS which is regarded as two of the approaches of modern artificial intelligence, to solve the problems of scheduling by single machine to minimize bi _ criteria $1/{r}_{j}/\displaystyle {\sum }_{j=1}^{n}{w}_{j}(1-{e}^{-r{c}_{j}})+{T}_{\max }$. This problem settled up to 30000 jobs.

A new generalizations of retractable modules relative to a submodule are introduced where a module is called retractable module relative to a submodule N of M if for all non-zero submodule K of such that contains N, there exists a non-zero homomorphism f∈Hom(, K). Some basic properties are studied and many relationships between these classes and other related concepts are presented and studied.

The purpose of this work is to determine the co-even domination number of various graphs, as a ladder, lollipop, butterfly, jellyfish, helm, corona, fan, and double fan graph. Before this, the important properties of the co-even dominating set are mentioned from previous work.

in this paper, the approximate solution of linear Fredholm integral equations of the second type on a closed interval is studied. The Galerkin method enhanced with Chebyshev polynomials was used to improve the approximate solution of our study, the related linear system was solved by the Boole's numerical integrated rule. for testing the efficiency of the proposed method, the comparison with related updated methods was executed.

In this paper, the notions of a Smarandache closed filter and Smarandache completely closed filter of a Smarandache BH-Algebra are introduced Also, Some properties of these notions are studied.

The asymptotic behavior for all nonoscillatory solutions for nonlinear neutral difference equations of third order has been investigated in this paper. Some necessary and sufficient conditions were obtained to ensure that these solutions are convergent to zero or divergent. There are some examples which illustrate our main findings.

In this paper, we stratify the connotation of cubic soft sets to ρ– algebras, and introduce the new class of cubic soft algebras like (e – CSp – SA) and (CSp – SA). We show that the R-union of two cubic soft ρ– sualgebras might not be cubic soft ρ– sualgebra. Furthermore, we show the sufficient condition to satisfy that the R-union of two cubic soft ρ– sualgebras is cubic soft ρ– sualgebra. Moreover, some of their basic characteristics are given.

A new extended mixed finite element method (MFEM) is suggested for parabolic integrodifferential equations (PIDEs) with nonlinear memory. On the contrary, of the extended mixed scheme, the modern extended mixed element system refers to an asymmetric positive well known and the two gradient equation as well as the flux equation can be isolated from the scalar undefined equation. The presence and uniqueness of the semi-discrete system can be confirmed and error estimates can be achieved for semidiscrete. Fully discrete can be said to be discretization.

In this paper, we apply a new technique, namely fractional Sumudu homotopy analysis method (FSHAM) on fractional partial differential equations to obtain the analytical approximate solutions. The fractional derivative is described in the Caputo sense. This method is the combination of the Sumudu transform (ST) and homotopy analysis method (HAM). The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.

The preset paper aims at finding the complete solution of certain types of linear partial differential equations of third order with constant coefficients that have three independent variables (q, r, s) of the general form: $\begin{array}{l}{A}_{1}{G}_{qqq}+{A}_{2}{G}_{qqr}+{A}_{3}{G}_{qrr}+{A}_{4}{G}_{qrr}+{A}_{4}{G}_{rrr}+{A}_{5}{G}_{qqs}+{A}_{6}{G}_{qss}+{A}_{7}{G}_{qrs}+{A}_{8}{G}_{rrs}+{A}_{9}{G}_{rss}+\\ {A}_{10}{G}_{sss}+{A}_{11}{G}_{qq}+{A}_{12}{G}_{qr}+{A}_{13}{G}_{qs}+{A}_{14}{G}_{rr}+{A}_{15}{G}_{rs}+{A}_{16}{G}_{ss}+{A}_{17}{G}_{q}+{A}_{18}{G}_{r}+\\ {A}_{19}{G}_{s}+{A}_{20}G=0\end{array}$ By using the assumption: G(q,r,s) = e^{∫y(q)dq + ∫x(r)dr + z(s)ds}, the above equation, according to this assumption, will be transformed to the non-linear second order ordinary differential equation with three independent functions. Thus, they have the general form: $\begin{array}{ll}{A}_{1}({y}^{^{\prime\prime} }+3y{y}^{^{\prime} } & +{y}^{3})+{A}_{2}(x{y}^{^{\prime} }+x{y}^{2})+{A}_{3}(y{x}^{^{\prime} }+y{x}^{2})+{A}_{4}({x}^{^{\prime\prime} }+3x{x}^{^{\prime} }+{x}^{3})\\ & +{A}_{5}(z{y}^{^{\prime} }+z{y}^{2})+{A}_{6}(y{z}^{^{\prime} }+y{z}^{2})+{A}_{7}yxz+{A}_{8}(z{x}^{^{\prime} }+z{x}^{2})\\ & +{A}_{9}(x{z}^{^{\prime} }+x{z}^{2})+{A}_{10}({z}^{^{\prime\prime} }+3z{z}^{^{\prime} }+{z}^{3})+{A}_{11}({y}^{^{\prime} }+{y}^{2})+{A}_{12}yx\\ & +{A}_{13}yz+{A}_{14}({x}^{^{\prime} }+{x}^{2})+{A}_{15}xz+{A}_{16}({z}^{^{\prime} }+{z}^{2})+{A}_{17}y+{A}_{18}x+{A}_{19}z\\ & +{A}_{20}=0\end{array}$

Note:- we used y instead of y(q) and χ instead of x(r) also ζ instead z(s).

In this paper, we will present a complementary algorithm for calculating the determinants order of n × n, ((n ≥ 5) Matrixes. This algorithm is based on the proposed ideal algorithm for permitting the fixing of two components. Programming this algorithm in Matlab as an application on permutations algorithms to finding determinants.

The generalization of the concept of inverse frame domination on graphs is the fundamental point of this work. It has been shown to present modern properties on inverse frame domination and some corresponding theorems related to delete, add edges or remove vertices. The relationship between the initial graph and a graph obtaining from the edges of the contraction was also discussed.

The purpose of this paper is to introduce a new inverse domination parameter in the graphs it is called inverse co-even domination number. Some properties of the theory to this definition were only touched. Also, many properties and limitations on this definition are determined. Additionally, some properties of inverse co-even domination number for some certain graphs and its complement are founded, such as regular, complete, path, cycle, wheel, complete bipartite, and star.

Since Newton time, Differential Equations have been used to comprehend most of physical, geometrical, and vital science in addition to their participation in the study of arithmetic analysis. Furthermore, they have been used in economical and social aspects. They have been developed and got significant position in various sciences. This paper presents for the non-homogeneous ordinary differential equations with the second order. This idea starts in chapter one which talks about the notion of those equations, their orders, in addition to the study of the linear differential equation with the first order and its solution. Whereas the second chapter studies the ordinary differential equations (homogeneous and non-homogeneous) and their solution. Each chapter is supported by solved examples that cover most of the aspects of the topic and we hope that this paper will make a good reference for those who would like to study this topic furtherly.

The aim of this paper is to study the concepts of the concepts of 2- anti fuzzy dominating (2 – AFD) set and 2- anti fuzzy domination number (2 – AF domination number) of an anti-fuzzy graph (G_AF).We determine the 2- anti fuzzy domination number (2 – AFD number γ_2AF) for some classes of an anti-fuzzy graphs (G_AF) and obtain the bounds on (2 – AFD number) for the same. The relations between (2 – AF domination number), anti fuzzy domination (AF domination number) and vertex anti-fuzzy vertex covering number (α₀) are discussed and found some result.

In this paper, we over the concept of doubt intuitionistic fuzzy d-algebra and the notation of doubt intuitionistic fuzzy semi d-ideal with various important properties, also we investigate some connection with a doubt intuitionistic fuzzy d-algebra .

In this paper, The notions of Q-Smarandache fuzzy implicative ideal and Q-Smarandache fuzzy sub implicative ideal of a Q-Smarandache BH-Algebra introduced, examples are given, and related properties investigated the relationships among these notions and other types of Q-Smarandache fuzzy ideal of a Q-Smarandache BH-Algebra are Studies.

In this paper we presented a new forms of maps called Nano-θG¹ closed, Nano-θG² closed, Nano-θG³ closed and Nano-θG⁴ closed in N-topological spaces and study the relationship between other current maps in N-topological spaces. A modern look of Homeomorphism named Nano-θG¹Homeomorphism is created and some of its characteristics are debated.

The aim of this article is to associate a tritopological space with undirected graph G = (V,E), i.e. three different topologies induced from the same graph or three different graphs. These tritopologies are the unique three proposed to associate topological spaces with graphs, the first which we proposed recently (Independent Topology) in 2020, the second is (Incidence Topology) proposed in 2018 and the third is proposed in 2013 (Graphic Topology). Then some properties of this tritopological space were investigated. Giving a fundamental step toward studying some properties of undirected graphs by their corresponding tritopological spaces is our motivation.

In the present paper the definitions of separation axioms in soft –tritopological spaces are introduced dependent to the soft – δ* – open set and their basic properties are investigated with respect to soft – points. That is, the soft – δ* – Ti; ( i = 0,1,2,3,4 ) spaces and notions of soft – δ* – normal and soft – δ* –regular spaces are discussed in detail, also we introduce some theorems shows how one of the soft –spaces implies the others with the help of an examples it is established that the converse does not hold.

In this paper the allocation of reliability and optimization has been calculated for each component of the complex system. Use (genetic algorithm) to solve the problem of allocation and to optimize system reliability. Also discussed are the three expense functions (exponential behavior with feasibility factor model, exponential behavior model and logarithmic model). The reliability importance of each component of the system was calculated after solving the allocation problem. The aim of this paper was to compare the results of the three cost functions by using GA in terms of reliability allocation and optimization, accurate reliability, reliability importance, and then whatever is more efficient than another.

In this paper, the authors studies new types of sets called β -sets in topological space (X. τ). We investigate and prove some topological properties and characterization of β-sets. Also, the relation between β- sets and open sets is discussed.

In this research, which contains three parameters, where a truncated state was taken from the left and a probability density function was found, as well as the moment function and the survival function, using the estimation method is the maximum likelihood estimation (MLE). And draw the figure of some of the mentioned functions using the Matlab program as well as estimating the values for the parameters.

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).

In this article, an efficient analytical technique, called Sumudu variational iteration method (SVIM), is used to obtain the solution of fractional partial differential equations arising in mathematical physics. The fractional derivatives are described in terms of Caputo sense. This method is the combination of the Sumudu transform (ST) and variational iteration method (VIM). The solution of the suggested technique is represented in a series form, which is convergent to the exact solution of the given problems. Furthermore, the results of the present method have shown close relations with the exact approaches of the investigated problems. Illustrative examples are discussed, showing the validity of the current method. The attractive and straightforward procedure of the present method suggests that this method can easily be extended for the solutions of other nonlinear fractional-order partial differential equations.

This work led to find the invariant factors of the tenser product ( ξ* (C α 3 )) and prove the general formula of $\unicode{x210C};\left(\begin{array}{l}\kappa \\ \otimes \end{array}\left(\equiv * \left({\text{C}}_{{\alpha }^{3}}\right)\right)\right)$

Let a continuous maps f:X → X, g:X → X be defined on a compact metric space X. We showed that f has bi-shadowing with g is equivalent to f has backwards bi-shadowing with g and f has two-sided bi-shadowing with g when the maps f, g are onto. We used this result to go on prove that, for expansive surjective maps f, g the properties f has bi-shadowing with g, f has two-sided bi-shadowing with g, f has s- limit bi-shadowing with g and f has two-sided s-limit bi-shadowing with g are equivalent. Finally we concluded that if a continuous maps f, g are surjective. Then f has two-sided s-limit bi-shadowing with g if and only if it has L-bi-shadowing with g.

The main objective of this research is to use methods of accelerating the first type of Al Tememe Acceleration, specifically triangular acceleration sine rule and triangular acceleration cosine rule which has the main error of the second level to find the continuous double integrations specified numerically with using the midpoint rule on both internal dimension t and exterior dimension z by both methods and we will code the first method with the symbol As(MM) and the second method the symbol Aco(MM) ;we assumed that the number of divisions on the internal dimension t was equal to the number of divisions on the external dimension z,where we got in both methods a high accuracy in the results with relatively few partial periods and a short time with the use of the Matlab 2017 program.

Our goal in this paper is introduce the action of hesienberg group on finite dimention manifold M. the interrelation ship between hesienberg group and the finite dimention manifold M is an old and vast subject. To simplify this treatment we work with liealgebra defined on a finite dimention manifold M, the heisenberg group forned an action over these liealgebra on finite manifold M.

No doubt, anotion on the heisnberg group can constitute avery important situation in the a differential finite manifold M, therefore, our work presents a key role mainly in some properties and characteriztions of the action of heinberg group on finite dimention manifold M, and also we study characterization on the relation between heisnberg group and finite dimention manifold M, then we introduce an an action of heisnberg group by the tensor product of the two repersentation which are (Acolyte groups) on hom (V₂, V₁') be the tensor product of two representations of heisberg group and construct the definition of AC-heisnberg group, also study the properties of this action.

The purpose of this study is investigate the Zariski topology of an involutory Q-algebra. We investigated new concepts of a Q-algebra, prime Q-filter, some properties of prime Q-filter in an involutory Q-algebra and investigate some basic properties of these concepts. In addition, the nation of the topology spectrum of an involutuory bounded Q-algebra was investigated. Moreover, we study some topological properties of a spectrum of an involutuory bounded Q-algebra

The trust region method is one of the important and effective ways to solve optimization problems due to its robust and accuracy in its convergence. One of its disadvantages is that its algorithm needs much time to solve its subproblems especially in the case of the problems that have a large-scale data. In this work, a new algorithm is suggested to solve this problem specifically subspace TRM. The initial TRR will be adequate to the subproblems which can be solved with a simple subspace, it will be simpler to solve than the classic TRM. The global convergence of the new method is investigated. The numerical results indicated that the new approach is promising.

In this paper special attention was focused on a system that cyclic paths and one terminal, this paper produces a new technique to evaluate the reliability system and how to make a special kind of equations to arrive to the reliability of each part of the system network.

The prediction of the urban population growth rate it gives estimate the expected change in the rate of growth in the future Based on socio-economic development and geography of the population, The use of time series analysis is one of the most important statistical methods used in the study and analysis of annual, monthly and daily data To prediction the values of future random phenomena based on what happened in the past which helps in making future plans for economic development. The goal of most of the statistical population studies is to provide an approximate forecast future population. In this paper, the Box-Jenkins models were compared to predict the rate of population growth in urban areas until the year (2033) based on the criterion of the mean absolute percentage error (MAPE) to choose the best prediction model.

In this study, some estimation methods (moments, modification moments, least square, weighted least square, maximum likelihood) were used to compare with each other the estimation of the parameters and reliability function of Transmuted Kumaraswamy (TK) distribution by using the simulation through four experiments (E₁,E₂, E₃, E₄) including the real values of the distribution parameters and by taking different sample sizes(n = 10,25,50,100). The comparison was done using the mean square error (MSE) criterion, and the results were set in special tables included research.