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7: Paper Source PDF document

Paper's Title:

Improved Oscillation Criteria of Second-Order Advanced Non-canonical Difference Equation

Author(s):

G. E. Chatzarakis1, N. Indrajith2, S. L. Panetsos1, E. Thandapani3

1Department of Electrical and Electronic Engineering Educators
School of Pedagogical and Technological Education,
Marousi 15122, Athens,
Greece.
E-mail: gea.xatz@aspete.gr, geaxatz@otenet.gr
spanetsos@aspete.gr

2Department of Mathematics,
Presidency College, Chennai - 600 005,
India.
E-mail: indrajithna@gmail.com

3Ramanujan Institute for Advanced Study in Mathematics,
University of Madras Chennai - 600 005,
India.
E-mail: ethandapani@yahoo.co.in

Abstract:

Employing monotonic properties of nonoscillatory solutions, we derive some new oscillation criteria for the second-order advanced non-canonical difference equation

Our results extend and improve the earlier ones. The outcome is illustrated via some particular difference equations.



4: Paper Source PDF document

Paper's Title:

Oscillatory Behavior of Second-Order Non-Canonical Retarded Difference Equations

Author(s):

G.E. Chatzarakis1, N. Indrajith2, E. Thandapani3 and K.S. Vidhyaa4

1Department of Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education,
Marousi 15122, Athens,
Greece.
E-mail:  gea.xatz@aspete.gr, geaxatz@otenet.gr

 

2Department of Mathematics,
Presidency College, Chennai - 600 005,
India.
E-mail: indrajithna@gmail.com

3Ramanujan Institute for Advanced Study in Mathematics,
University of Madras,
Chennai - 600 005,
India.
E-mail: ethandapani@yahoo.co.in

4Department of Mathematics,
SRM Easwari Engineering College,
Chennai-600089,
India.
E-mail: vidyacertain@gmail.com

Abstract:

Using monotonic properties of nonoscillatory solutions, we obtain new oscillatory criteria for the second-order non-canonical difference equation with retarded argument

Our oscillation results improve and extend the earlier ones. Examples illustrating the results are provided.



3: Paper Source PDF document

Paper's Title:

On the Oscillatory Behavior of Self Adjoint Fractional Extensible Beam Equations

Author(s):

S. Priyadharshini1, G.E. Chatzarakis2, S. L. Panetsos2 and V. Sadhasivam1

1Post Graduate and Research Department of Mathematics,
Thiruvalluvar Government Arts College,
Rasipuram - 637 401, Namakkal Dt., Tamil Nadu,
India.
E-mail: s.priya25april@gmail.com, ovsadha@gmail.com

2Department of Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education(ASPETE),
Marousi 15122, Athens,
Greece.
E-mail: geaxatz@otenet.gr, gea.xatz@aspete.gr, spanetsos@aspete.gr

Abstract:

The main objective of this paper is to study the oscillatory behavior of the solutions of self adjoint fractional extensible beam equations by using integral average method. Some new sufficient conditions are established with various boundary conditions over a cylindrical domains. Examples illustrating the results are given.



3: Paper Source PDF document

Paper's Title:

ℵ0 Algebra and its Novel Application in Edge Detection

Author(s):

G. E. Chatzarakis1, S. Dickson2, S. Padmasekaran2, S. L. Panetsos1, and J. Ravi3

1Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education (ASPETE),
Marousi 15122, Athens,
Greece.
E-mail: geaxatz@otenet.gr, spanetsos@aspete.gr

2Mathematics, Periyar University,
Periyar Palkalai Nagar, Salem, 636011, Tamilnadu,
India.
E-mail: dix.bern@gmail.com, padmasekarans@periyaruniversity.ac.in

3Department of Mathematics, Amity University,
Bengaluru, Karnataka,
India.
E-mail: jravistat@gmail.com
 

Abstract:

In this paper a new type of ℵ0-algebra has been defined. With its help, the fuzzy cross subalgebra and the fuzzy η-relation on the ℵ0-algebra are introduced and their respective properties are derived. Moreover, the fuzzy cross ℵ0-ideal of the ℵ0-algebra is defined with some theorems and intuitionistic fuzzy ℵ0-ideals of the ℵ0-algebra are introduced. This fuzzy algebra concept is applied in image processing to detect edges. This ℵ0-algebra is a novelty in the field of research.



3: Paper Source PDF document

Paper's Title:

Oscillation Criteria for Second Order Delay Difference Equations via Canonical Transformations and Some New Monotonic Properties

Author(s):

R. Deepalakhmi, S. Saravanan, J. R. Graef, and E. Thandapani

Department of Interdisciplinary Studies
Tamil Nadu Dr. Ambedkar Law University
Chennai-600113,
India.
profdeepalakshmi@gmail.com

Madras School of Economics,
Chennai-600025,
India.
profsaran11@gmail.com

Department of Mathematics,
University of Tennessee at Chattanooga,
Chattanooga,TN 37403,
USA.
john-graef@utc.edu

Ramanujan Institute for Advanced Study in Mathematics,
University of Madras,
Chennai - 600 005,
India.
ethandapani@yahoo.co.in

Abstract:

This paper is concerned with second-order linear noncanonical delay difference equations of the form

Δ(μ(t)Δ y(t))+ p(t)y(φ(t))=0.

The authors prove new oscillation criteria by first transforming the equation into canonical form and then obtaining some new monotonic properties of the positive solutions of the transformed equation. By using a comparison with first-order delay difference equations and a generalization of a technique developed by Koplatadze, they obtain their main results. Examples illustrating the improvement over known results in the literature are presented.



2: Paper Source PDF document

Paper's Title:

Oscillations of First Order Linear Delay Difference Equations

Author(s):

G. E. Chatzarakis and I. P. Stavroulakis

Department of Mathematics, University of Ioannina,
451 10, Greece
ipstav@cc.uoi.gr


Abstract:

Consider the first order linear delay difference equation of the form   where  is a sequence of nonnegative real numbers, k is a positive integer and  denotes the forward difference operator  New oscillation criteria are established when the well-known oscillation conditions  and  are not satisfied. The results obtained essentially improve known results in the literature.



2: Paper Source PDF document

Paper's Title:

SQIRV Model for Omicron Variant with Time Delay

Author(s):

S. Dickson, S. Padmasekaran, G. E. Chatzarakis and S. L. Panetsos

Mathematics, Periyar University, Periyar Palkalai Nagar, Salem,
636011, Tamilnadu,
India.
E-mail: dickson@periyaruniversity.ac.in, padmasekarans@periyaruniversity.ac.in

Electrical and Electronic Engineering Educators, School of
Pedagogical and Technological Education (ASPETE),
Marousi 15122, Athens,
Greece.
E-mail: geaxatz@otenet.gr, spanetsos@aspete.gr

Abstract:

In order to examine the dynamics of the Omicron variant, this paper uses mathematical modelling and analysis of a SQIRV model, taking into account the delay in the conversion of susceptible individuals into infected individuals and infected individuals into recovered individuals. The pandemic was eventually controlled as a result of the massive delays. To assure the safety of the host population, this concept incorporates quarantine and the COVID-19 vaccine. Both local and global stability of the model are examined. It is found that the fundamental reproduction number affects both local and global stability conditions. Our findings show that asymptomatic cases caused by an affected population play an important role in increasing Omicron infection in the general population. The most recent data on the pandemic Omicron variant from Tamil Nadu, India, is verified.



2: Paper Source PDF document

Paper's Title:

Semicommutative and Semiprime Properties in Bi-amalgamated Rings

Author(s):

1A. Aruldoss, 2C. Selvaraj, 3G. E. Chatzarakis, 4S. L. Panetsos, 5U. Leerawat

1 Department of Mathematics,
Mepco Schlenk Engineering College,
Sivakasi-626 005, Tamilnadu,
India.
aruldossa529@gmail.com

2 Department of Mathematics,
Periyar University,
Salem - 636 011, Tamilnadu,
India.
selvavlr@yahoo.com

 3,4 Department of Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education (ASPETE),
Marousi 15122, Athens,
Greece.
geaxatz@otenet.gr spanetsos@aspete.gr

5 Department of Mathematics,
Faculty of Science, Kasetsart University,
Bangkok 10900,
Thailand.
fsciutl@ku.ac.th

Abstract:

Let α: A B and β: A C be two ring homomorphisms and I and I' be two ideals of B and C, respectively, such that α{-1}(I)=β{-1}(I'). In this paper, we give a characterization for the bi-amalgamation of A with (B, C) along (I, I') with respect to (α, β) (denoted by A⋈(α, β)(I, I')) to be a SIT, semiprime, semicommutative and semiregular. We also give some characterization for these rings.



2: Paper Source PDF document

Paper's Title:

Robust Layer Resolving Scheme for a System of Two Singularly Perturbed Time-Dependent Delay Initial Value Problems with Robin Initial Conditions

Author(s):

1K. Ramiya Bharathi, 2G. E. Chatzarakis, 2S. L. Panetsos, and 1M. Joseph Paramasivam

1PG & Research Department of Mathematics,
Bishop Heber College (Affiliated to Bharathidasan University),
Tiruchirappalli - 620 017, Tamil Nadu,
India.
E-mail: ramiyabharathik28@gmail.com, paramasivam.ma@bhc.edu.i 

2Department of Electrical and Electronic Engineering Educators,
School of Pedagogical \& Technological Education (ASPETE),
Marousi, 15122, Athens,
Greece.
E-mail: gea.xatz@aspete.gr, spanetsos@aspete.gr

Abstract:

This paper aimed at proving first order convergence for system of two singularly perturbed time-dependent initial value problems with delay in spatial variable and robin initial conditions. A Classical layer resolving finite difference scheme is developed by implementing uniform mesh for time discretization; Shishkin-mesh, a piecewise uniform mesh for spatial discretization. Shishkin-mesh is constructed is such way it captures the intricacies behavior of the layers. The interior layer is induced by the presence of a delay term in the space term. Error estimate is carried out to prove first order convergence with the help of maximum principle, stability analysis, solution bounds and sharper estimates of the singular components of the solutions. Finally, the numerical illustration is computed for the problem to bolster the scheme.



1: Paper Source PDF document

Paper's Title:

Linear System of Singularly Perturbed Initial Value Problems with Robin Initial Conditions

Author(s):

S. Dinesh, G. E. Chatzarakis, S. L. Panetsos and S. Sivamani

Department of Mathematics,
Saranathan College of Engineering,
Tiruchirappalli-620012,
Tamil Nadu,
India.

Department of Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education,
Marousi 15122, Athens,
Greece.

E-mail: geaxatz@otenet.gr, dineshselvaraj24@gmail.com,
spanetsos@aspete.gr, winmayi2012@gmail.com

Abstract:

On the interval (0,1], this paper considers an initial value problem for a system of n singularly perturbed differential equations with Robin initial conditions. On a piecewise uniform Shishkin mesh, a computational approach based on a classical finite difference scheme is proposed. This approach is shown to be first-order convergent in the maximum norm uniformly in the perturbation parameters. The theory is illustrated by a numerical example.


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