The Australian Journal of Mathematical Analysis and Applications

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5: Paper Source PDF document

Paper's Title:

Integer Sums of Powers of Trigonometric Functions (MOD p), for prime p


G. J. Tee

Department of Mathematics, University of Auckland, Auckland,
New Zealand


Many multi--parameter families of congruences (mod p) are found for integer sums of  qth powers of the trigonometric functions over various sets of equidistant arguments, where p is any prime factor of q. Those congruences provide sensitive tests for the accuracy of software for evaluating trigonometric functions to high precision.

3: Paper Source PDF document

Paper's Title:

SQIRV Model for Omicron Variant with Time Delay


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

Mathematics, Periyar University, Periyar Palkalai Nagar, Salem,
636011, Tamilnadu,

Electrical and Electronic Engineering Educators, School of
Pedagogical and Technological Education (ASPETE),
Marousi 15122, Athens,


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.

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