Normalized laplacian spectrum of two new types of join graphs
M.
Hakimi-Nezhaad
Department of Mathematics, Faculty of Science, Shahid Rajaee
Teacher Training University, Tehran, 16785-136, Iran
author
M.
Ghorbani
Department of Mathematics, Faculty of Science, Shahid Rajaee
Teacher Training University, Tehran, 16785-136, Iran
author
text
article
2017
eng
Let $G$ be a graph without an isolated vertex, the normalized Laplacian matrix $\tilde{\mathcal{L}}(G)$ is defined as $\tilde{\mathcal{L}}(G)=\mathcal{D}^{-\frac{1}{2}}\mathcal{L}(G)\mathcal{D}^{-\frac{1}{2}}$, where $\mathcal{D}$ is a diagonal matrix whose entries are degree of vertices of $G$. The eigenvalues of $\tilde{\mathcal{L}}(G)$ are called as the normalized Laplacian eigenvalues of $G$. In this paper, we obtain the normalized Laplacian spectrum of two new types of join graphs. In continuing, we determine the integrality of normalized Laplacian eigenvalues of graphs. Finally, the normalized Laplacian energy and degree Kirchhoff index of these new graph products are derived.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch. IAU
2252-0201
06
v.
01
no.
2017
1
9
http://jlta.iauctb.ac.ir/article_530214_bbc846be4c0a7da114894aa6723fc11b.pdf
The method of radial basis functions for the solution of nonlinear Fredholm integral equations system.
J.
Nazari
Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University,
Isfahan, Iran
author
M.
Nili Ahmadabadi
Department of Mathematics, Najafabad Branch, Islamic Azad University,
Najafabad, Iran
author
H.
Almasieh
Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University,
Isfahan, Iran
author
text
article
2017
eng
In this paper, An effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (RBFs). We present an algorithm based on interpolation by radial basis functions including multiquadratics (MQs), using Legendre-Gauss-Lobatto nodes and weights. Also a theorem is proved for convergence of the algorithm. Some numerical examples are presented and results are compared to the analytical solution and Triangular functions (TF), Delta basis functions (DFs), block-pulse functions , sinc fucntions, Adomian decomposition, computational, Haar wavelet and direct methods to demonstrate the validity and applicability of the proposed method.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch. IAU
2252-0201
06
v.
01
no.
2017
11
28
http://jlta.iauctb.ac.ir/article_530220_dff904fa08b1056450c1a5a5977c0379.pdf
Unique common coupled fixed point theorem for four maps in $S_b$-metric spaces
K. P. R.
Rao
Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar,
Guntur-522 510, Andhra Pradesh, India
author
G. V. N.
Kishore
Department of Mathematics, K L University, Vaddeswaram, Guntur-522 502,
Andhra Pradesh, India
author
Sk.
Sadik
Department of Mathematics, Sir C R R College of Engineering, Eluru,
West Godavari-534 007, Andhra Pradesh, India
author
text
article
2017
eng
In this paper we prove a unique common coupled fixed point theorem for two pairs of $w$-compatible mappings in $S_b$-metric spaces satisfying a contrctive type condition. We furnish an example to support our main theorem. We also give a corollary for Junck type maps.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch. IAU
2252-0201
06
v.
01
no.
2017
29
43
http://jlta.iauctb.ac.ir/article_530217_56934be0fc2de05532e4acfcd9699735.pdf
Coupled fixed point theorems involving contractive condition of integral type in generalized metric spaces
R.
Shah
Department of Mathematics, University of Peshawar, Peshawar, Pakistan
author
A.
Zada
Department of Mathematics, University of Peshawar, Peshawar, Pakistan
author
text
article
2017
eng
In this manuscript, we prove some coupled fixed point theorems for two pairs of self mappings satisfying contractive conditions of integral type in generalized metric spaces. We furnish suitable illustrative examples. In this manuscript, we prove some coupled fixed point theorems for two pairs of self mappings satisfying contractive conditions of integral type in generalized metric spaces. We furnish suitable illustrative examples.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch. IAU
2252-0201
06
v.
01
no.
2017
45
53
http://jlta.iauctb.ac.ir/article_530218_9ce6588837690e14ec3335854e50166b.pdf
Characterization of $\delta$-double derivations on rings and algebras
A.
Hosseini
Department of Mathematics, Kashmar Higher Education Institute, Kashmar, Iran
author
text
article
2017
eng
The main purpose of this article is to offer some characterizations of $\delta$-double derivations on rings and algebras. To reach this goal, we prove the following theorem:Let $n > 1$ be an integer and let $\mathcal{R}$ be an $n!$-torsion free ring with the identity element $1$. Suppose that there exist two additive mappings $d,\delta:R\to R$ such that $$d(x^n) =\Sigma^n_{j=1} x^{n-j}d(x)x^{j-1}+\Sigma^{n-2}_{k=0} \Sigma^{n-2-k}_{i=0} x^k\delta(x)x^i\delta(x)x^{n-2-k-i}$$ is fulfilled for all $x\in \mathcal{R}$. If $\delta(1) = 0$, then $d$ is a Jordan $\delta$-double derivation. In particular, if $\mathcal{R}$ is a semiprime algebra and further, $\delta^2(x^2) = \delta^2(x)x + x\delta^2(x) + 2(\delta(x))^2$ holds for all $x\in \mathcal{R}$, then $d-\frac{1}{2}\delta^2$ is an ordinary derivation on $\mathcal{R}$.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch. IAU
2252-0201
06
v.
01
no.
2017
55
65
http://jlta.iauctb.ac.ir/article_530219_27c0141510309a0b0e9c5e4e2896400c.pdf
Computational aspect to the nearest southeast submatrix that makes multiple a prescribed eigenvalue
A.
Nazari
Department of Mathematics, Arak University,
P.O. Box 38156-8-8349, Arak, Iran
author
A.
Nezami
Department of Mathematics, Arak University,
P.O. Box 38156-8-8349, Arak, Iran
author
text
article
2017
eng
Given four complex matrices $A$, $B$, $C$ and $D$ where $A\in\mathbb{C}^{n\times n}$ and $D\in\mathbb{C}^{m\times m}$ and let the matrix $\left(\begin{array}{cc} A & B \ C & D \end{array} \right)$ be a normal matrix and assume that $\lambda$ is a given complex number that is not eigenvalue of matrix $A$. We present a method to calculate the distance norm (with respect to 2-norm) from $D$ to the set of matrices $X \in C^{m \times m}$ such that, $\lambda$ be a multiple eigenvalue of matrix $\left(\begin{array}{cc} A & B \ C & X \end{array} \right)$. We also find the nearest matrix $X$ to the matrix $D$.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch. IAU
2252-0201
06
v.
01
no.
2017
11
28
http://jlta.iauctb.ac.ir/article_530216_a502b7f8619b310d41d7a1432359e88d.pdf
New best proximity point results in G-metric space
A. H.
Ansari
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
author
A.
Razani
Department of Mathematics, Faculty of Science, Imam Khomeini
International University, postal code: 34149-16818, Qazvin, Iran
author
N.
Hussain
Department of Mathematics, King Abdulaziz University,
P.O. Box 80203, Jeddah 21589, Saudi Arabia
author
text
article
2017
eng
Best approximation results provide an approximate solution to the fixed point equation $Tx=x$, when the non-self mapping $T$ has no fixed point. In particular, a well-known best approximation theorem, due to Fan cite{5}, asserts that if $K$ is a nonempty compact convex subset of a Hausdorff locally convex topological vector space $E$ and $T:K\rightarrow E$ is a continuous mapping, then there exists an element $x$ satisfying the condition $d(x,Tx)=\inf \{d(y,Tx):y\in K\}$, where $d$ is a metric on $E$. Recently, Hussain et al. (Abstract and Applied Analysis, Vol. 2014, Article ID 837943) introduced proximal contractive mappings and established certain best proximity point results for these mappings in $G$-metric spaces. The aim of this paper is to introduce certain new classes of auxiliary functions and proximal contraction mappings and establish best proximity point theorems for such kind of mappings in $G$-metric spaces. As consequences of these results, we deduce certain new best proximity and fixed point results in $G$-metric spaces. Moreover, we present certain examples to illustrate the usability of the obtained results.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch. IAU
2252-0201
06
v.
01
no.
2017
73
89
http://jlta.iauctb.ac.ir/article_530221_121e115915de0dbaa0e435e6c44729b0.pdf