Archive:: Pure and Applied Mathematics Journal:: Science Publishing Group

Volume 5, Issue 5, October 2016

A Comparative Study Between Laplace Transform and Two New Integrals “ELzaki” Transform and “Aboodh” Transform

Abdelbagy A. Alshikh, Mohand M. Abdelrahim Mahgob

Issue: Volume 5, Issue 5, October 2016

Pages: 145-150

Received: 7 August 2016

Accepted: 20 August 2016

Published: 7 September 2016

DOI: 10.11648/j.pamj.20160505.11

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Abstract: In this paper we discuss some relationship between Laplace transform and the new two transform called ELzaki transform and Aboodh transform. We solve first and second order ordinary differential equations using both transforms, and show that ELzaki transform and Aboodh transform are closely connected with the Laplace transform.

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An Application of the New Integral “Aboodh Transform” in Cryptography

Abdelilah K. Hassan Sedeeg, Mohand M. Abdelrahim Mahgoub, Muneer A. Saif Saeed

Issue: Volume 5, Issue 5, October 2016

Pages: 151-154

Received: 7 August 2016

Accepted: 23 August 2016

Published: 9 September 2016

DOI: 10.11648/j.pamj.20160505.12

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Abstract: Cryptography is the science of providing security for information, It has been used historically as a means of providing secure communication between individuals. Message encryption has become very essential to avoid the threat against possible attacks by hackers during transmission process of the message. In this paper authors have proposed a meth... Show More

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A Note on Strict Commutativity of a Monoidal Product

Youngsoo Kim

Issue: Volume 5, Issue 5, October 2016

Pages: 155-159

Received: 25 August 2016

Accepted: 5 September 2016

Published: 21 September 2016

DOI: 10.11648/j.pamj.20160505.13

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Abstract: It is well known that a monoidal category is (monoidally) equivalent to a strict monoidal category that is a monoidal category with a strictly associative product. In this article, we discuss strict commutativity and prove a necessary and sufficient condition for a symmetric monoidal category to be equivalent to another symmetric monoidal category ... Show More

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Inverse Vector Function Hilbert Boundary Value Problem

Ding Yun, Yang Xiaochun

Issue: Volume 5, Issue 5, October 2016

Pages: 160-164

Received: 28 August 2016

Accepted: 9 September 2016

Published: 28 September 2016

DOI: 10.11648/j.pamj.20160505.14

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Abstract: In the paper, how to solve an irregular vector function Hilbert boundary value inverse problem is discussed in generalization. In the solving, some diagonal matrices are introduced for helping to regulate those equations of Hilbert boundary value problem. Then, the solution of the problem is given.

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Pentacyclic Harmonic Graph

Ahmad Salehi Zarrin Ghabaei, Shahroud Azami

Issue: Volume 5, Issue 5, October 2016

Pages: 165-173

Received: 28 August 2016

Accepted: 8 September 2016

Published: 11 October 2016

DOI: 10.11648/j.pamj.20160505.15

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Abstract: Let be a graph on n vertices and let be the degree of vertex A graph is defined to be harmonic if is an eigenvector of the -adjacency matrix of We now show that there are 4 regular and 45 non-regular connected pentacyclic harmonic graphs and determine their structure. In the end we conclude that all of c-cyclic harmonic graphs for are planar graphs.

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