Pure and Applied Mathematics Journal

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
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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.
  • 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
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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
  • 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
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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
  • 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
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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.
  • 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
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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.