Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 6 1 2021 08 01 Coupled Fixed Point Theorems in G-metric Spaces via Α-series 1 12 191 10.22128/gadm.2021.374.1031 EN Samira Hadi Bonab Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran Rasoul Abazari Department of Mathematics, Ardabil Branch Islamic Azad University, Ardabil, Iran Ali Bagheri Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran Hasan Hosseinzadeh Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran 0000-0002-1723-4140 Journal Article 2020 09 12 The object of this paper is to study of the results of coupled fixed point in generalized metric spaces, as known as G-metric spaces. We will impose some conditions upon a self-mapping and a sequence of mappings via a kind of series, known as a-series. Also, an example is provided to illustrate the results.

https://ansne.du.ac.ir/article_191_3bdedd3ded6fbc8847ba54f6cccf95f8.pdf

Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 6 1 2021 08 01 On Left φ-biflat and Left φ-biprojectivity of θ-lau Product Algebras 13 23 192 10.22128/gadm.2020.380.1033 EN Amir Sahami Department of Mathematics, Faculty of Basic Sciences Ilam University P.O. Box 69315-516 Ilam, Iran. 0000-0003-0041-509X Sayed Mehdi Kazemi Torbaghan Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran. Journal Article 2020 10 09 \textit{Monfared} defined $\theta$-Lau product structure $A\times_{\theta} B$ for two Banach algebras $A$ and $B$, where $\theta:B\rightarrow \mathbb{C} $ is a multiplicative linear functional. In this paper, we study the notion of left $\phi$-biflatness and left $\phi$-biprojectivity for the $\theta$ Lau product structure $A\times_{\theta} B$. For a locally compact group $G$, we show that $M(G)\times_{\theta}M(G)$ is left character biflat (left character biprojective) if and only if $G$ is discrete and amenable ($G$ is finite), respectively. Also we prove that $\ell^{1}(\Bbb{N}_{\vee})\times_{\theta}\ell^{1}(\Bbb{N}_{\vee})$ is neither $(\phi_{\Bbb{N}_{\vee}}, \theta)$-biprojective nor $ (0, \phi_{\Bbb{N}_{\vee}})$-biprojective, where $\phi_{\Bbb{N}_{\vee}}$ is the augmentation character on $\ell^{1}(\Bbb{N}_{\vee}).$ Finally, we give an example among the Lau product structure of matrix algebras which is not left $\phi$-biflat.

https://ansne.du.ac.ir/article_192_e0b08a20a6576b83cc53393bdae68fa9.pdf

Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 6 1 2021 08 01 Upper and Lower Central Series in a Pair of Lie Algebras 25 31 193 10.22128/gadm.2020.381.1034 EN Fatemeh Pazandeh Sh. School of Mathematics and Computer sciences, Damghan University, Damghan, Iran Asadollah Faramarzi Salles Damghan University Journal Article 2020 10 10 The Baer's theorem in the termes of the Lie algebras states that for a Lie algebra $L$ the finiteness of $\mathrm{dim}(L/Z_i(L))$ implies the finiteness of $\mathrm{dim}(\gamma_{i+1}(L))$. Let $(N,L)$ denote a pair of Lie algebras, where $N$ is an ideal of $L$, and $d_i=d_i(L)$ denote the minimal number of generators of $L/Z_i(N, L)$. In this paper we shall consider the pair $(N, L)$ and show that if $d_n$ is finite then the converse of Baer's theorem is true. In fact we shall show that if $d_n$ and $\mathrm{dim}(\gamma_{i+1}(N, L))$ are finite, where $i\geq n$, then $N/Z_i(N, L))$ is finite. In particular, we shall provide an upper bound as following, $$\mathrm{dim}(\frac{N}{Z_i(N, L)}) \leq ((d_n)^nd_nd_{n+1}\ldots d_{i-1})\mathrm{dim}(\gamma_{i+1}(N, L))$$$$\leq (d_n)^i(\mathrm{dim}\gamma_{i+1}(N, L)).$$ for all non negative integers i.

https://ansne.du.ac.ir/article_193_2614a731cf7843d6fe5c0df5d760c0bb.pdf

Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 6 1 2021 08 01 Close-to-Regularity of Bounded Tri-Linear Maps 33 39 194 10.22128/gadm.2021.382.1035 EN Abotaleb Sheikhali Independent Researcher. Kazem Haghnejad Azar Department of Mathematics and Applications, University of Mohaghegh Ardabili, Ardabi, Iran. Ali Ebadian Department of Mathematics , University of Urmia, Urmia, Iran. Journal Article 2020 11 10 Let f : X × Y × Z → W be a bounded tri-linear map on normed spaces. We say that f is close-to-regular when ft∗∗∗∗s = fs∗∗∗∗t and we say that f is Aron-Berner regular when all natural extensions are equal. In this manuscript, we give a simple criterion for the close-to-regularity of tri-linear maps.

https://ansne.du.ac.ir/article_194_ab621b87838d95e31d9cb4f72f82b0c3.pdf

Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 6 1 2021 08 01 An Iterative Method for Solving Two Dimensional Nonlinear Volterra Integral Equations 41 57 195 10.22128/gadm.2021.383.1036 EN Manochehr Kazemi Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran 0000-0001-8392-6690 Journal Article 2020 11 22 In this paper, a numerical iterative algorithm based on combination of the successive approximations method and the quadrature formula for solving two-dimensional nonlinear Volterra integral equations is proposed. This algorithm uses a trapezoidal quadrature rule for Lipschitzian functions applied at each iterative step. The convergence analysis and error estimate of the method are proved. Finally, two numerical examples are presented to show the accuracy of the proposed method.

https://ansne.du.ac.ir/article_195_81e88c6657d11588350c1deb1094e8ca.pdf

Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 6 1 2021 08 01 Numerical Solution of Degenerate Fourth Order SDE Model by Milstein Scheme 59 71 196 10.22128/gadm.2021.384.1037 EN Daryoush Kalvand Department of Mathematics,Linnaeus University,351 95,Vaxjo,Sweden Esmaeil Yousefi Department of Mathematics, Islamic Azad University, Karaj Branch, Iran Journal Article 2020 11 26 In this paper, we use a Milstein scheme to develop a numerical technique for solving Stochastic differential equation which we had its deterministic form in our last article [7], we discuss the existence and uniqueness solution of deterministic and stochastic form, and then we show the advantages of the method with numerical example.

https://ansne.du.ac.ir/article_196_b308137e43893f55d4f75e1368b4b4e1.pdf

Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 6 1 2021 08 01 Some Remarks on the Varieties of Pairs of Groups 73 81 197 10.22128/gadm.2021.393.1040 EN Homayoon Arabyani Department of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran; Tel.: +123-45-678910 Fax: +123-45-678910 Journal Article 2021 02 27 Let V be a variety of groups defined by a set v of laws .Let (N,G) be a pair of groups in which N is a normal subgroup of G. we define the lower and upper V-marginal series of the pair (N,G) and prove some results on the varieties nilpotent pais of groups. Moreover, we extend some properties of the Baer-invariant and isologism of a pairs of groups.

https://ansne.du.ac.ir/article_197_a3efb25d6d66e50dba1ffa7231fb1e7c.pdf

Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 6 1 2021 08 01 Ray Casting Based Volume Rendering of Medical Images 83 98 198 10.22128/gadm.2021.394.1041 EN Maryam Ghobadi school of mathematics and computer science, Damghan university Arash Azimzadeh Irani school of mathematics and computer science, Damghan university Journal Article 2021 03 06 - The goal of 3-D visualization is to provide the user with an intuitive interface which enables him to explore the 3-D data. The rapid development in information technology has immensely contributed to the use of modern approaches for visualizing volumetric data. Consequently, medical volume visualization is increasingly attracting attension towards achieving an effective visualization algorithm for medical diagnosis and pre-treatment planning. Previously, research has been addressing implementation of algorithm that can visualize 2-D images into 3-D. Meanwhile, in medical diagnosis, finding the exact diseases location is an important step of surgery / disease management. For 3-D Medical Data, Magnetic Resonance Images (MRI) have been used to create the 3D model, we used the Direct Volume Rendering technique. This paper proposes a ray casting algorithm for accurate allocation and localization of human abdomen abnormalities using magnetic resonance images (Abdomen MRI) of normal and abnormal patients.

https://ansne.du.ac.ir/article_198_0bab262270f7a40e3ac17e01ea3d912b.pdf

Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 6 1 2021 08 01 The Schultz and the Modified Schultz Indices of Kragujevac Trees 99 108 208 10.22128/gadm.2021.408.1045 EN Abbas Heydari Arak Uinversity of Technology, Arak, Iran. Journal Article 2021 04 28 Let G be simple connected graph with the vertex and edge sets V(G) and E(G), respectively. The Schultz and Modified Schultz indices of a connected graph G are defined as Sc(G) =1/2 ∑u,v∈V(G) (du + dv)d(u,v) and Sc*(G) = 1\2∑u,v∈ V(du×dv)d(u, v), where d(u, v) is the topological distance between vertices u and v, dv is the degree of vertex v of G. In this paper, computation of the Schultz and Modified Schultz indices of the Kragujevac trees is proposed. As application, we obtain an upper bound and a lower bound for the Schultz and the modified Schultz indices of this tree.

https://ansne.du.ac.ir/article_208_8b96e66b3e98da5c42f3b3eb39c07ff1.pdf

Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 6 1 2021 08 01 Soft G-Metric Spaces for Fixed Point Theorems 109 129 209 10.22128/gadm.2021.395.1042 EN Khelghat Amini Sefidab Department of Mathematics, Ardabil Branch Islamic Azad University, Ardabil, Iran Hasan Hosseinzadeh Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran 0000-0002-1723-4140 Ali Bagheri Vakilabad Islamic Azad Univercity Ardabil Rasoul Abazari Department of Mathematics, Ardabil Branch Islamic Azad University, Ardabil, Iran Journal Article 2021 03 12 In this article, we the concept of soft G-metric space and continuous soft mapping on it introduce. We also the Banach fixed point theorem in complete soft G-metric spaces investigate.

https://ansne.du.ac.ir/article_209_80a3acba4db620a3aa090337e80e8d5f.pdf

Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 6 1 2021 08 01 Perfect 4-Colorings of the 3-Regular Graphs of Order 10 131 142 210 10.22128/gadm.2021.439.1048 EN Zeinab Vahedi Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran Mohammad Maghasedi Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran 0000-0001-6551-6620 Mehdi Alaeiyan Iran University of Science and Technology 0000-0003-2185-5967 Journal Article 2021 07 26 The perfect m-coloring with matrix A = [aij ]i,j∈{1,...,m} of a graph G = (V, E) with {1, . . . , m} color is a vertices coloring of G with m-color so that number of vertex in color j adjacent to a fixed vertex in color i is aij , independent of the choice of vertex in color i. The matrix A = [aij ]i,j∈{1,...,m} is called the parameter matrix. We study the perfect 4-colorings of the 3-regular graphs of order 10, that is, we determine a list of all color parameter matrices corresponding to perfect colorings of 3-regular graphs of order 10.

https://ansne.du.ac.ir/article_210_611fc6cb4f723872135a7b02c25d70ee.pdf

Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 6 1 2021 08 01 Prediction of Fuzzy Nonparametric Regression Function: A Comparative Study of a New Hybrid Method and Smoothing Methods 143 177 211 10.22128/gadm.2021.387.1038 EN Mahdi Danesh Imam Khomeini International University – Buin Zahra Higher Education Center of Engineering and Technology, Buein Zahra, Ghazvin, Iran Sedigheh Danesh Young Researchers and Elite Club, East Tehran Branch, Islamic Azad university, Tehran, Iran. Tahereh Razzaghnia Department of statistics, North Tehran Branch, Islamic Azad University, Tehran, Iran 0000-0002-5870-8381 Ali Maleki Department of Statistics, West Tehran Branch, Islamic Azad University, Tehran, Iran Journal Article 2021 01 07 In this paper, the fuzzy regression model is considered with crisp inputs and symmetric triangular fuzzy output. This study aims to formulate the fuzzy inference system based on the Sugeno inference model for the fuzzy regression function prediction by the fuzzy least-squares problem-based on Diamond's distance. In this study, the fuzzy least-squares problem is used to optimize consequent parameters, and the results are derived based on the V-fold cross-validation, so that the validity and quality of the proposed method can be guaranteed. The proposed method is used to reduce the bias and the boundary effect of the estimated underlying regression function. Also, a comparative study of the fuzzy nonparametric regression function prediction is carried out between the proposed model and smoothing methods, such as k-nearest neighbor (k-NN), kernel smoothing (KS), and local linear smoothing (LLS). Different approaches are illustrated by some examples and the results are compared. Comparing the results indicates that, among the various prediction models, the proposed model is the best, decreasing the boundary effect significantly. Also, in comparison with different methods, in both one-dimensional and two-dimensional inputs, it may be considered the best candidate for the prediction.

https://ansne.du.ac.ir/article_211_58ae2f672f88a375cbcb909be98c7a8e.pdf