Serdica Mathematical Journal
Volume 47, Number 4, 2021
C O N T E N T S
·
Arthi, K., R. Sangeetha, C. Sankari.
S4-decomposition of the line graph of the complete graph
(pp. 273−284)
·
Chande, M. K.
Modified ElGamal signature with secret key pair and additional random number
(pp. 285−290)
·
Sakaki, M., A. Uçum.
On generalized helicoidal minimal surfaces in Minkowski 5-space
(pp. 291−304)
·
Jeena, M. S., L. Sebastian.
A general existence principle for fixed point theorems
in one parameter case of soft Da-metric space
(pp. 305−316)
·
Askour, N. E., Z. Mouhcine.
Heat and resolvent kernels and a fundamental solution
for the octonionic Heisenberg Laplacian
(pp. 317−342)
A B S T R A C T S
S4-DECOMPOSITION OF THE LINE GRAPH OF THE COMPLETE GRAPH
K. Arthi
arthi1505@gmail.com
R. Sangeetha
jaisangmaths@yahoo.com
C. Sankari
sankari9791@gmail.com
2020 Mathematics Subject Classification:
05C70, 05C76.
Key words:
Decomposition, induced subgraph, line graph, complete graph, star.
Let Sk denote a star with k edges. The line graph of the complete graph Kn is denoted by L(Kn). In this paper, we prove that the graph L(Kn) has an S4-decomposition if and only if n ≥ 6 and n ≡ 0, 1, 2, 4, 6 (mod 8).
MODIFIED ELGAMAL SIGNATURE WITH SECRET KEY PAIR AND ADDITIONAL RANDOM NUMBER
Manoj Kumar Chande
manojkumarchande@gmail.com
2020 Mathematics Subject Classification:
94A60.
Key words:
ElGamal signature scheme, discrete logarithm problem, random number.
ElGamal digital signature has numerous applications in real time situations. Due to its utility and popularity, security threats and challenges are increasing day by day for this signature scheme. This paper introduces a variant of ElGamal signature scheme, mainly after analyzing the existing weaknesses of the scheme where the security depends on one private key only. To overcome this, our scheme consists of a private key pair and an additional random number which makes the relation between the secret key and the randomly chosen number used more complicated. The cryptographic security of the proposed scheme is relatively much higher than the existing ElGamal signature scheme in literature.
ON GENERALIZED HELICOIDAL MINIMAL SURFACES IN MINKOWSKI 5-SPACE
Makoto Sakaki
sakaki@hirosaki-u.ac.jp
Ali Uçum
aliucum05@gmail.com
2020 Mathematics Subject Classification:
53C42, 53C50.
Key words:
Minkowski 5-space, helicoidal surface, minimal surface.
In this paper, we study two kinds of generalized helicoidal surfaces in
Minkowski 5-space. We give the necessary and sufficient conditions for
such surfaces to be a minimal surface, which are ordinary differential
equations. We solve those equations explicitly and discuss the behavior of
solutions.
A GENERAL EXISTENCE PRINCIPLE FOR FIXED POINT THEOREMS IN ONE PARAMETER CASE OF SOFT Da-METRIC SPACE
M. S. Jeena
jeenams99@gmail.com
Lovelymol Sebastian
lovelymaths95@gmail.com
2020 Mathematics Subject Classification:
47H10,54H25,54E99.
Key words:
Soft set, soft metric, D-metric, soft D-metric, fixed point theorem.
In this article we define orbit and related terminologies for soft sets. We prove some fixed point results for soft Da- metric space in a specific orbital case and extending various general principles for fixed point theorems in Da-metric space to soft Da-metric spaces.
HEAT AND RESOLVENT KERNELS AND A FUNDAMENTAL SOLUTION FOR THE OCTONIONIC HEISENBERG LAPLACIAN
Nour Eddine Askour
n.askour@usms.ma
Zakariyae Mouhcine
zakariyaemouhcine@gmail.com
2020 Mathematics Subject Classification:
22E25, 22E30, 35K08.
Key words:
Octonionic Heisenberg group. Kohn's Laplacian, fundamental solution, heat kernel, resolvent kernel, Whittaker function.
We give an integral representation of the fundamental solution of the heat and resolvent equations associated to the Kohn's Laplacian on the octonionic Heisenberg group. Moreover, the fundamental solution for the octonionic Heisenberg Laplacian is found.
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