eng
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
2017-06-01
06
01
1
9
530214
Normalized laplacian spectrum of two new types of join graphs
M. Hakimi-Nezhaad
m.hakimi20@gmail.com
1
M. Ghorbani
mghorbani@srttu.edu
2
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-136, Iran
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-136, Iran
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.
http://jlta.iauctb.ac.ir/article_530214_bbc846be4c0a7da114894aa6723fc11b.pdf
join of graphs
normalized Laplacian eigenvalue
integral eigenvalue
eng
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
2017-06-01
06
01
11
28
530220
The method of radial basis functions for the solution of nonlinear Fredholm integral equations system.
J. Nazari
jinoosnazari@yahoo.com
1
M. Nili Ahmadabadi
mneely59@hotmail.com
2
H. Almasieh
3
Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran
Department of Mathematics, Najafabad Branch, Islamic Azad University, Najafabad, Iran
Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran
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.
http://jlta.iauctb.ac.ir/article_530220_dff904fa08b1056450c1a5a5977c0379.pdf
Radial basis functions
Fredholm integral equations system
eng
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
2017-06-01
06
01
29
43
530217
Unique common coupled fixed point theorem for four maps in $S_b$-metric spaces
K. P. R. Rao
kprrao2004@yahoo.com
1
G. V. N. Kishore
kishore.apr2@gmail.com
2
Sk. Sadik
sadikcrrce@gmail.com
3
Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar, Guntur-522 510, Andhra Pradesh, India
Department of Mathematics, K L University, Vaddeswaram, Guntur-522 502, Andhra Pradesh, India
Department of Mathematics, Sir C R R College of Engineering, Eluru, West Godavari-534 007, Andhra Pradesh, India
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.
http://jlta.iauctb.ac.ir/article_530217_56934be0fc2de05532e4acfcd9699735.pdf
$S_b$-metric space
$w$-compatible pairs
$S_b$-completeness
coupled fixed point
eng
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
2017-06-01
06
01
45
53
530218
Coupled fixed point theorems involving contractive condition of integral type in generalized metric spaces
R. Shah
safeer_rahim@yahoo.com
1
A. Zada
2
Department of Mathematics, University of Peshawar, Peshawar, Pakistan
Department of Mathematics, University of Peshawar, Peshawar, Pakistan
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.
http://jlta.iauctb.ac.ir/article_530218_9ce6588837690e14ec3335854e50166b.pdf
Generalized metric space
coupled fixed points
integral type contractive mapping
Fixed point
eng
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
2017-06-01
06
01
55
65
530219
Characterization of $delta$-double derivations on rings and algebras
A. Hosseini
hosseini.amin82@gmail.com
1
Department of Mathematics, Kashmar Higher Education Institute, Kashmar, Iran
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 $d,delta:Rto R$ such that $$d(x^n) =Sigma^n_{j=1} x^{n-j}d(x)x^{j-1}+Sigma^{n-2}_{k=0} Sigma^{n-2-k}_{i=0} x^kdelta(x)x^idelta(x)x^{n-2-k-i}$$ is fulfilled for all $xin mathcal{R}$. If $delta(1) = 0$, then $d$ is a Jordan $delta$-double derivation. In particular, if $mathcal{R}$ is a semiprime algebra and further, $delta^2(x^2) = delta^2(x)x + xdelta^2(x) + 2(delta(x))^2$ holds for all $xin mathcal{R}$, then $d-frac{1}{2}delta^2$ is an ordinary derivation on $mathcal{R}$.
http://jlta.iauctb.ac.ir/article_530219_27c0141510309a0b0e9c5e4e2896400c.pdf
$delta$-Double derivation
Jordan $delta$-double derivation
$n$-torsion free semiprime ring
eng
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
2017-06-01
06
01
11
28
530216
Computational aspect to the nearest southeast submatrix that makes multiple a prescribed eigenvalue
A. Nazari
a-nazari@araku.ac.ir
1
A. Nezami
2
Department of Mathematics, Arak University, P.O. Box 38156-8-8349, Arak, Iran
Department of Mathematics, Arak University, P.O. Box 38156-8-8349, Arak, Iran
Given four complex matrices $A$, $B$, $C$ and $D$ where $Ainmathbb{C}^{ntimes n}$ and $Dinmathbb{C}^{mtimes m}$ 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 $D$.
http://jlta.iauctb.ac.ir/article_530216_a502b7f8619b310d41d7a1432359e88d.pdf
Normal matrix
multiple eigenvalues
singular value
distance matrices
eng
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
2017-06-01
06
01
73
89
530221
New best proximity point results in G-metric space
A. H. Ansari
analsisamirmath2@gmail.com
1
A. Razani
razani@sci.ikiu.ac.ir
2
N. Hussain
nhusain@kau.edu.sa
3
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
Department of Mathematics, Faculty of Science, Imam Khomeini International University, postal code: 34149-16818, Qazvin, Iran
Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
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 $T:Krightarrow E$ is a continuous mapping, then there exists an element $x$ satisfying the condition $d(x,Tx)=inf {d(y,Tx):yin K}$, 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.
http://jlta.iauctb.ac.ir/article_530221_121e115915de0dbaa0e435e6c44729b0.pdf
Best proximity point
Generalized proximal weakly G-contraction
G-metric space