Serdica Mathematical Journal
Volume 47, Number 2, 2021
C O N T E N T S
·
Argyros, I. K., S. George.
Extending the convergence region of m-step iterative procedures
(pp. 93−107)
·
Aydın, E.
Non-tame automorphisms of free polynilpotent Lie algebrass
(pp. 108−112)
·
Ebrahimi Atani, S., M. Chenari.
Closed weak supplemented property in the lattices
(pp. 113−128)
·
AL-dheleai, F. S., E. M. Elabbasy.
New oscillation criteria for third order nonlinear mixed neutral dynamic equations
(pp. 129−152)
·
Choudhry, A.
A Diophantine problem concerning third order matrices
(pp. 153−160)
·
Tiwari, S. K., P. Porwal, T. Barve.
Transmission dynamics of coronavirus and the effect of vaccination using SEIR model
(pp. 161−178)
A B S T R A C T S
EXTENDING THE CONVERGENCE REGION OF M-STEP ITERATIVE PROCEDURES
Ioannis K. Argyros
iargyros@cameron.edu
Santhosh George
sgeorge@nitk.edu.in
2020 Mathematics Subject Classification:
65F08, 37F50, 65N12.
Key words:
m-step iterative methods, Banach space, semi-local convergence, Newton's method, Lipschitz continuity.
The convergence region of iterative procedures is small in general, and it becomes smaller as m increases. This problem limits the choice of starting points, and consequently the applicability of these methods. The novelty of this work lies in the fact that, we extend the convergence region by using specializations of the Lipschitz constants used before. Further advantages include improved error estimations and uniqueness results. The results are tested favorably to us on examples.
NON-TAME AUTOMORPHISMS OF FREE POLYNILPOTENT LIE ALGEBRAS
Ela Aydın
eaydin@cu.edu.tr
2020 Mathematics Subject Classification:
17B01, 17B30, 17B40.
Key words:
IA-automorphisms, non-tame automorphisms.
Let L be a free Lie algebra generated by x and y over an arbitrary field K of any characteristic and let V be an ideal of L of the form V = (...((Lkm)km − 1)...)k1, ki ≥ 2, i = 1, ..., m , m ≥ 2, i.e. L/V is a non-trivial 2-generated free polynilpotent Lie algebra. We have established that the algebra L/V has non-tame IA-automorphisms.
CLOSED WEAK SUPPLEMENTED PROPERTY IN THE LATTICES
Shahabaddin Ebrahimi Atani
Sándor Szabó
ebrahimi@guilan.ac.ir
Maryam Chenari
chenari.maryam13@gmail.com
2020 Mathematics Subject Classification:
06C05, 06C15.
Key words:
Lattice, filter, small, closed weak supplemented.
Let L be a lattice with the greatest element 1. Following the concept of closed weak supplemented modules, we define closed weak supplemented filters and we will make an intensive investigate the basic properties and possible structures of these filters.
NEW OSCILLATION CRITERIA FOR THIRD ORDER NONLINEAR MIXED
NEUTRAL DYNAMIC EQUATIONS
Faisal Saleh AL-dheleai
faisalsaleh69@yahoo.com
Elmetwally Mohammed Elabbasy
emelabbasy@mans.edu.eg
2020 Mathematics Subject Classification:
34K11, 39A10, 34N05.
Key words:
Oscillatory solutions, third order, neutral, dynamic
equation, mixed argument.
In this work, some new oscillation criteria are established for a third order nonlinear mixed neutral dynamic equation. Our
results improve and extend some known results in the literature. Several
examples are given to illustrate the importance of the results.
A DIOPHANTINE PROBLEM CONCERNING THIRD ORDER MATRICES
Ajai Choudhry
ajaic203@yahoo.com
2020 Mathematics Subject Classification:
Primary: 15B36;
Secondary: 11C20, 11D25, 11D41.
Key words:
unimodular matrix; third order matrix; third order determinant.
In this paper we find a third order unimodular matrix, none of whose entries is 1 or −1, such that when each entry of the matrix is replaced by its cube, the resulting matrix is also unimodular. Further, we find third order square integer matrices (aij), none of the integers aij being 1 or −1, such that det(aij) = k and det(aij3) = k3, where k is a nonzero integer.
TRANSMISSION DYNAMICS OF CORONAVIRUS AND THE EFFECT OF VACCINATION USING SEIR MODEL
Sandeep Kumar Tiwari
skt_tiwari75@yahoo.co.in
Pradeep Porwal
pradeepratnawat@yahoo.com
Trupti Barve
truptibarve23@gmail.com
2020 Mathematics Subject Classification:
34A34, 34D20, 34D23.
Key words:
Covid-19, vaccination, disease free equilibrium, stability analysis, sensitivity analysis, basic reproduction number.
In the present paper, an SEIR mathematical model has been discussed to study the transmission dynamics of the coronavirus and the impact of vaccination in which infected individuals have been classified based on vaccination status. Local stability and global stability analysis have been done for the disease free equilibrium state. It is observed that the disease free equilibrium state is local asymptotically stable when R0 < 1. Sensitivity analysis has been performed and the effects of different classes of infected individuals have been studied. It has been found that the basic reproduction number shows the highest sensitivity towards the nonvaccinated class of infected individuals as compared to other infected classes. Analytical results have been expressed graphically.
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