Research Paper Combinatorics, Graph theory
2. Self-dual double cyclic codes over $\mathbb{Z}_2$H. Movahedi; L. Pourfaraj
Volume 10, Issue 04 , Autumn 2021, Pages 257-267
Abstract A double cyclic code [or \emph{DC code}] of length $n=k+l$ over $\mathbb{Z}_2$ is a binary linear code, where any cyclic shift of the first $k$ coordinates and the last $l$ coordinates of a codeword is also a codeword. In this paper, we study the relationship between separability and self-duality of ... Read More A double cyclic code [or \emph{DC code}] of length $n=k+l$ over $\mathbb{Z}_2$ is a binary linear code, where any cyclic shift of the first $k$ coordinates and the last $l$ coordinates of a codeword is also a codeword. In this paper, we study the relationship between separability and self-duality of these codes. Also, we obtain the shadow code by determining the generator polynomials of the doubly even subcode of the self-dual code.
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Research Paper Linear and multilinear algebra; matrix theory
3. Inverse eigenvalue problem for bordered diagonal matricesS. Mashayekhi; S. M. Karbassi; S. A. Shahzadefazeli
Volume 10, Issue 04 , Autumn 2021, Pages 269-276
Abstract In this paper, the inverse eigenvalue problem for the bordered diagonal matrices are reconsidered whose elements are equal to zero except for the first row, the first column and the diagonal elements. The necessary and sufficient conditions for existence of a symmetric bordered diagonal matrix from ... Read More In this paper, the inverse eigenvalue problem for the bordered diagonal matrices are reconsidered whose elements are equal to zero except for the first row, the first column and the diagonal elements. The necessary and sufficient conditions for existence of a symmetric bordered diagonal matrix from special spectral data have been determined. A new algorithm to make such matrices is derived and some numerical examples are given to illustrate the efficiency of the method.
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Review paper Functional analysis
6. Convergence, stability and data dependence results for contraction and nonexpansive mappings by a new four step algorithmU. E. Udofia; D. Igbokwe
Volume 10, Issue 04 , Autumn 2021, Pages 295-321
Abstract Here we show that the UI-iteration scheme [Udofia and Igbokwe, [24]] can be used to approximate the fixed points of contraction and nonexpansive mappings. we prove a strong and weak convergence of the iteration scheme to the fixed point of contraction and nonexpansive mappings. We also prove that the ... Read More Here we show that the UI-iteration scheme [Udofia and Igbokwe, [24]] can be used to approximate the fixed points of contraction and nonexpansive mappings. we prove a strong and weak convergence of the iteration scheme to the fixed point of contraction and nonexpansive mappings. We also prove that the scheme is Γ-stable and data dependent. Analytically and with numerical example we show that the UI-iteration scheme has a faster rate of convergence for contraction and nonexpansive mappings than some well known existing iteration schemes in literature. Finally, we apply the UI-iteration scheme to find the solution of constrained convex minimization problem.
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Research Paper Fixed point theory
7. Coincident and common fixed point theorems using comparison and admissible function in w-distance metric spaceS. Arora; M. Masta
Volume 10, Issue 04 , Autumn 2021, Pages 323-333
Abstract In this manuscript, the concept of generalized $[\eta, \chi, p]$ contractive mapping for two maps in the framework of w-distance is introduced and some fixed point results are established, which extend recent results of Lakzian and Rhoades [5] and many existing results ... Read More In this manuscript, the concept of generalized $[\eta, \chi, p]$ contractive mapping for two maps in the framework of w-distance is introduced and some fixed point results are established, which extend recent results of Lakzian and Rhoades [5] and many existing results in the literature. In addition, to validate the novelty of our findings, we give an illustrative example, which yields the main result. Moreover, as an application, we employ the achieved result to earn the existence criteria of the solution of a type of non-linear Fredholm integral equation.
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Calculus of variations and optimal control; optimization
1. The directional hybrid measure of efficiency in data envelopment analysisA. Mirsalehy; M. Rizam Abu Baker; L. S. Lee; Gh. R. Jahanshahloo
Volume 05, Issue 03 , Summer 2016, , Pages 155-174
Abstract The efficiency measurement is a subject of great interest. The majority of studies on DEA models have been carried out using radial or non-radial approaches regarding the application of DEA for the efficiency measurement. This paper, based on the directional distance function, proposes a new generalized ... Read More The efficiency measurement is a subject of great interest. The majority of studies on DEA models have been carried out using radial or non-radial approaches regarding the application of DEA for the efficiency measurement. This paper, based on the directional distance function, proposes a new generalized hybrid measure of efficiency under generalized returns to scale with the existence of both radial and non-radial inputs and outputs. It extends the hybrid measure of efficiency from Tone [2004] to a more general case. The proposed model is not only flexible enough for the decision-maker to adjust the radial and non-radial inputs and outputs to attain the efficiency score but also avoids the computational and interpretive difficulties, thereby giving rise to an important clarification and understanding of the generalized DEA model. Furthermore, several frequently-used DEA models [such as the CCR, BCC, ERM and SBM models] which depend on the radial or non-radial approaches are derived while their results were compared to the ones obtained from this hybrid model. The empirical examples emphasize the consequence of the proposed measure.
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Research Paper Operator theory
1. Reverses of the first Hermite-Hadamard type inequality for the square operator modulus in Hilbert spacesS. S. Dragomir
Articles in Press, Accepted Manuscript, Available Online from 25 January 2022
Abstract Let $\left[ H;\left\langle \cdot ,\cdot \right\rangle \right]$ be a complex Hilbert space. Denote by $\mathcal{B}\left[ H\right]$ the Banach $C^{\ast }$-algebra of bounded linear operators on $H$. For $A\in \mathcal{B}\left[H\right]$ we define the ... Read More Let $\left[ H;\left\langle \cdot ,\cdot \right\rangle \right]$ be a complex Hilbert space. Denote by $\mathcal{B}\left[ H\right]$ the Banach $C^{\ast }$-algebra of bounded linear operators on $H$. For $A\in \mathcal{B}\left[H\right]$ we define the modulus of $A$ by $\left\vert A\right\vert :=\left[A^{\ast }A\right] ^{1/2}$ and \ $\func{Re}A:=\frac{1}{2}\left[ A^{\ast}+A\right].$ In this paper we show among other that, if $A,$ $B\in \mathcal{B}\left[ H\right]$ with $0\leq m\leq \left\vert \left[ 1-t\right]A+tB\right\vert ^{2}\leq M$ for all $t\in \left[ 0,1\right],$ then \begin{align*} 0& \leq \int_{0}^{1}f\left[ \left\vert \left[ 1-t\right] A+tB\right\vert^{2}\right] dt-f\left[ \frac{\left\vert A\right\vert ^{2}+\func{Re}\left[B^{\ast }A\right] +\left\vert B\right\vert ^{2}}{3}\right] \\ & \leq 2\left[ \frac{f\left[ m\right] +f\left[ M\right] }{2}-f\left[ \frac{m+M}{2}\right] \right] 1_{H} \end{align*} for operator convex functions $f:[0,\infty ]\rightarrow \mathbb{R}$. Applications for power and logarithmic functions are also provided.
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