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2024

Vol 2, No 2 (2024)

Vol 2, No 1 (2024)

2023

Vol 1, No 1 (2023)

Featured Articles

Why the big bang never happened

If general relativity is correct, then the origin of the universe is a simple mathematical problem. The Friedmann equation in cosmology is a well-structured ordinary diﬀerential equation, and the global properties of its solutions can be qualitatively analyzed by the phase-trajectory method. In this paper we show that the total energy density of matter in the universe is positive, and the total pressure near the Big Bang is negative. By analyzing the global properties of the solutions to the Friedmann equation according to these two conditions of state functions, we ﬁnd that the Big Bang is impossible, and the space must be a closed 3-dimensional sphere, the cosmological constant is likely to be zero, and the evolution of the universe should be cyclic. The analysis and the proof are simple and straight forward, therefore these conclusions should be reliable.

Fermat surfaces and hypercubes

Fermat’s last theorem appears not as a unique property of natural numbers but as the bottom line of extended possible issues involving larger dimensions and powers when observed from a natural vector space viewpoint. The fabric of this general Fermat’s theorem structure consists of a well-defined set of vectors associated with dimensional vector spaces and the Minkowski norms one can define there. Here, a special vector set is studied and named a Fermat surface. Besides, a connection between Fermat surfaces and hypercubes is unveiled.

Approximation results of Phillips type operators including exponential function

Prerna Sharma, Diwaker Sharma

Article ID: 2821
Vol 2, Issue 2, 2024

DOI: https://doi.org/10.54517/mss.v2i2.2821

Received: 9 July 2024; Accepted: 24 September 2024; Available online: 6 October 2024;
Issue release: 15 November 2024

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Abstract

The current article deals with a study on some moderation of the Phillips operators, including constant and exponential functions. Here, we derive the moments applying the notion of moment-generating function for the well-known Phillips operators. The authors also establish uniform convergence estimates for the improved form of these operators. Additionally, some direct estimates involving the asymptotic-type results are discussed.

Keywords

Phillips operators; approximation; exponential functions; moments; linear positive operators

References

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3. Abel U, Gupta V. The rate of convergence of a generalization of Post–Widder operators and Rathore operators. Advances in Operator Theory. 2023; 8(3). doi: 10.1007/s43036-023-00272-y

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Cairo University, Egypt

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2024-09-20

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Since the journal launch in 2023, we have been proud to publish a plethora of insightful findings in the realms of mathematics and systems science....

2024-07-10

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It is with great pride that we introduce Prof. Youssri Hassan Youssri and Prof. Ali Akgül, who are the Editor-in-Chief and Associate Editor of our esteemed journal.

2024-01-05

Articles in the First Issue of Volume 1 - Now Available Online

We are delighted to announce that the articles in the first issue of Volume 1 of Mathematics and Systems Science is now live and accessible online.

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