OMS – Vol 8 – 2024 – PISRT https://old.pisrt.org Fri, 23 Aug 2024 08:56:41 +0000 en-US hourly 1 https://wordpress.org/?v=6.6.2 Annular structures in perturbed low mass disc-shaped gaseous nebulae: general, standard and polytropic models https://old.pisrt.org/psr-press/journals/oms-vol-8-2024/annular-structures-in-perturbed-low-mass-disc-shaped-gaseous-nebulae-general-standard-and-polytropic-models/ Sun, 28 Jul 2024 07:49:28 +0000 https://old.pisrt.org/?p=8416
OMS-Vol. 8 (2024), Issue 1, pp. 55-82 Open Access Full-Text PDF
Vladimir Pletser
Abstract:We study analytical solutions of a bi-dimensional low-mass gaseous disc slowly rotating around a central mass and submitted to small radial periodic perturbations. Hydrodynamics equations are solved for the equilibrium and perturbed configurations. A wave-like equation for the gas-perturbed specific mass is deduced and solved analytically for several cases of exponents of the power law distributions of the unperturbed specific mass and sound speed. It is found that, first, the gas perturbed specific mass displays exponentially spaced maxima, corresponding to zeros of the radial perturbed velocity; second, the distance ratio of successive maxima of the perturbed specific mass is a constant depending on disc characteristics and, following the model, also on the perturbation's frequency; and, third, inward and outward gas flows are induced from zones of minima toward zones of maxima of perturbed specific mass, leading eventually to the possible formation of gaseous annular structures in the disc. The results presented may be applied in various astrophysical contexts to slowly rotating thin gaseous discs of negligible relative mass, submitted to small radial periodic perturbations. ]]>
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Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 55-82
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2024.0226

Annular structures in perturbed low mass disc-shaped gaseous nebulae: general, standard and polytropic models

Vladimir Pletser\(^{1,2*}\)
\(^{1}\) lnstitut d’Astronomie et de Geophysique G.Lemaitre, Catholic University of Louvain, Louvain-la-Neuve, Belgium
\(^{2}\) Blue Abyss, Newquay, Cornwall, United Kingdom

Copyright © 2024 Vladimir Pletser. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: April 6, 2023 – Accepted: July 22, 2024 – Published: July 28, 2024

Abstract

We study analytical solutions of a bi-dimensional low-mass gaseous disc slowly rotating around a central mass and submitted to small radial periodic perturbations. Hydrodynamics equations are solved for the equilibrium and perturbed configurations. A wave-like equation for the gas-perturbed specific mass is deduced and solved analytically for several cases of exponents of the power law distributions of the unperturbed specific mass and sound speed. It is found that, first, the gas perturbed specific mass displays exponentially spaced maxima, corresponding to zeros of the radial perturbed velocity; second, the distance ratio of successive maxima of the perturbed specific mass is a constant depending on disc characteristics and, following the model, also on the perturbation’s frequency; and, third, inward and outward gas flows are induced from zones of minima toward zones of maxima of perturbed specific mass, leading eventually to the possible formation of gaseous annular structures in the disc. The results presented may be applied in various astrophysical contexts to slowly rotating thin gaseous discs of negligible relative mass, submitted to small radial periodic perturbations.

Keywords:

Fluid dynamics; Hydrodynamics; Protoplanetary nebulae
]]> A version of the Hermite-Hadamard inequality for Quasi \(F-(h,g,m)\)-convex functions https://old.pisrt.org/psr-press/journals/oms-vol-8-2024/a-version-of-the-hermite-hadamard-inequality-for-quasi-f-hgm-convex-functions/ Sun, 28 Jul 2024 07:41:34 +0000 https://old.pisrt.org/?p=8414
OMS-Vol. 8 (2024), Issue 1, pp. 46-54 Open Access Full-Text PDF
Ghulam Farid and Josip Pečarić
Abstract:This paper aims to present Hermite-Hadamard type inequalities for a new class of functions, which will be denoted by \(Q_m^{h,g}(F;I)\) an and called class of quasi \(F-(h,g;m)\)-convex functions defined on interval \(I\). Many well known classes of functions can be recaptured from this new quasi convexity in particular cases. Also, several publish results are obtained along with new kinds of inequalities.]]>
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Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 46-54
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2024.0225

A version of the Hermite-Hadamard inequality for Quasi \(F-(h,g,m)\)-convex functions

Ghulam Farid\(^{1,*}\) and Josip Pečarić\(^{2}\)
\(^{1}\) Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan
\(^{2}\) Croatian Academy of Sciences and Arts, Zagreb, Croatia

Copyright © 2024 Ghulam Farid and Josip Pečarić. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: November 22, 2023 – Accepted: May 11, 2024 – Published: June 30, 2024

Abstract

This paper aims to present Hermite-Hadamard type inequalities for a new class of functions, which will be denoted by \(Q_m^{h,g}(F;I)\) an and called class of quasi \(F-(h,g;m)\)-convex functions defined on interval \(I\). Many well known classes of functions can be recaptured from this new quasi convexity in particular cases. Also, several publish results are obtained along with new kinds of inequalities.

Keywords:

Convex function; \((h,g;m)\)-convex function; Hermite-Hadamard inequality
]]> On the semilocal convergence analysis of a seventh order four step method for solving nonlinear equations https://old.pisrt.org/psr-press/journals/oms-vol-8-2024/on-the-semilocal-convergence-analysis-of-a-seventh-order-four-step-method-for-solving-nonlinear-equations/ Sun, 30 Jun 2024 03:30:41 +0000 https://old.pisrt.org/?p=8319
OMS-Vol. 8 (2024), Issue 1, pp. 39-45 Open Access Full-Text PDF
Samundra Regmi , Ioannis K. Argyros , Santhosh George and Christopher I. Argyros
Abstract:We provide a semi-local convergence analysis of a seventh order four step method for solving nonlinear problems. Using majorizing sequences and under conditions on the first derivative, we provide sufficient convergence criteria, error bounds on the distances involved and uniqueness. Earlier convergence results have used the eighth derivative not on this method to show convergence. Hence, limiting its applicability.]]>
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Open Journal of Mathematical Sciences
Vol. 8 (2024), Issue 1, pp. 39-45
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2024.0224

On the semilocal convergence analysis of a seventh order four step method for solving nonlinear equations

Samundra Regmi\(^{1}\), Ioannis K. Argyros\(^{2,*}\), Santhosh George\(^{3}\) and Christopher I. Argyros\(^{4}\)
\(^{1}\) European Space Research and Technology Centre (ret.); Current address: Blue Abyss, Newquay, Cornwall, United Kingdom; Pletservladimir@gmail.com

Copyright © 2024 Samundra Regmi , Ioannis K. Argyros , Santhosh George and Christopher I. Argyros. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: March 19, 2022 – Accepted: April 06, 2024 – Published: June 30, 2024

Abstract

We provide a semi-local convergence analysis of a seventh order four step method for solving nonlinear problems. Using majorizing sequences and under conditions on the first derivative, we provide sufficient convergence criteria, error bounds on the distances involved and uniqueness. Earlier convergence results have used the eighth derivative not on this method to show convergence. Hence, limiting its applicability.

Keywords:

Banach space; convergence order; Iterative method.
]]> Distribution of Prime Numbers and Fibonacci Polynomials https://old.pisrt.org/psr-press/journals/oms-vol-8-2024/distribution-of-prime-numbers-and-fibonacci-polynomials/ Thu, 16 May 2024 04:08:05 +0000 https://old.pisrt.org/?p=8317
OMS-Vol. 8 (2024), Issue 1, pp. 31-38 Open Access Full-Text PDF
Vladimir Pletser
Abstract:Squares of odd index Fibonacci polynomials are used to define a new function \(\Phi\left(10^{n}\right)\) to approximate the number \(\pi\left(10^{n}\right)\) of primes less than \(10^{n}\). Multiple of 4 index Fibonacci polynomials are further used to define another new function \(\Psi\left(10^{n}\right)\) to approximate the number \(\Delta\left(\pi\left(10^{n}\right)\right)\) of primes having \(n\) digits and compared to a third function \(\Psi'\left(10^{n}\right)\) defined as the difference of the first function \(\Phi\left(10^{n}\right)\) based on odd index Fibonacci polynomials. These three functions provide better approximations of \(\pi\left(10^{n}\right)\) than those based on the classical \(\left(\frac{x}{log\left(x\right)}\right)\), Gauss' approximation \(Li\left(x\right)\), and the Riemann \(R\left(x\right)\) functions.]]>
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Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 31-38
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2024.0223

Distribution of prime numbers and Fibonacci polynomials

Vladimir Pletser\(^{1,*}\)
\(^{1}\) European Space Research and Technology Centre (ret.); Current address: Blue Abyss, Newquay, Cornwall, United Kingdom; Pletservladimir@gmail.com

Copyright © 2024 Vladimir Pletser. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: June 14, 2023 – Accepted: April 06, 2024 – Published: May 15, 2024

Abstract

Squares of odd index Fibonacci polynomials are used to define a new function \(\Phi\left(10^{n}\right)\) to approximate the number \(\pi\left(10^{n}\right)\) of primes less than \(10^{n}\). Multiple of 4 index Fibonacci polynomials are further used to define another new function \(\Psi\left(10^{n}\right)\) to approximate the number \(\Delta\left(\pi\left(10^{n}\right)\right)\) of primes having \(n\) digits and compared to a third function \(\Psi’\left(10^{n}\right)\) defined as the difference of the first function \(\Phi\left(10^{n}\right)\) based on odd index Fibonacci polynomials. These three functions provide better approximations of \(\pi\left(10^{n}\right)\) than those based on the classical \(\left(\frac{x}{log\left(x\right)}\right)\), Gauss’ approximation \(Li\left(x\right)\), and the Riemann \(R\left(x\right)\) functions.

Keywords:

{Distribution of Prime Numbers; Fibonacci Numbers; Fibonacci Polynomials
]]> Euler’s and the taxi cab relations and other numbers that can be written twice as sums of two cubed integers https://old.pisrt.org/psr-press/journals/oms-vol-8-2024/eulers-and-the-taxi-cab-relations-and-other-numbers-that-can-be-written-twice-as-sums-of-two-cubed-integers/ Thu, 16 May 2024 03:54:15 +0000 https://old.pisrt.org/?p=8312
OMS-Vol. 8 (2024), Issue 1, pp. 25-30 Open Access Full-Text PDF
Vladimir PLETSER
Abstract:We show that Euler's relation and the Taxi-Cab relation are both solutions of the same equation. General solutions of sums of two consecutive cubes equaling the sum of two other cubes are calculated. There is an infinite number of relations to be found among the sums of two consecutive cubes and the sum of two other cubes, in the form of two families. Their recursive and parametric equations are calculated.]]>
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Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 25-30
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2024.0222

Euler’s and the taxi cab relations and other numbers that can be written
twice as sums of two cubed integers

Vladimir PLETSER\(^{1,*}\)
\(^{1}\) European Space Agency (ret.); Pletservladimir@gmail.com

Copyright © 2024 Vladimir PLETSER. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: March 4, 2022 – Accepted: April 06, 2024 – Published: May 15, 2024

Abstract

We show that Euler’s relation and the Taxi-Cab relation are both solutions of the same equation. General solutions of sums of two consecutive cubes equaling the sum of two other cubes are calculated. There is an infinite number of relations to be found among the sums of two consecutive cubes and the sum of two other cubes, in the form of two families. Their recursive and parametric equations are calculated.

Keywords:

Sums of two consecutive cubes ; Equal sums of two cubes ; Taxi-Cab
number ; Euler’s relation
]]> An estimate of the rate of convergence of infinite matrices and their application to infinite series https://old.pisrt.org/psr-press/journals/oms-vol-8-2024/existence-and-convergence-of-gamma-matrices-and-their-application-to-infinite-series/ Wed, 15 May 2024 17:02:43 +0000 https://old.pisrt.org/?p=8310
OMS-Vol. 8 (2024), Issue 1, pp. 17-24 Open Access Full-Text PDF
Suresh Kumar Sahani, A.K. Thakur, Avinash Kumar and K. Sharma
Abstract:This study introduces theorems concerning matrix products, which delineate the transformations of sequences or series into other sequences or series, ensuring either the preservation of limits or the guarantee of convergence. Previous literature has explored the properties of matrices facilitating transformations between sequences, series, and their combinations, with detailed insights available in references [1,2,3].]]>
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Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 17-24
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2024.0221

An estimate of the rate of convergence of infinite matrices and their application to infinite series

Suresh Kumar Sahani\(^{1}\), A.K. Thakur\(^{2}\), Avinash Kumar\(^{3}\) and K. Sharma\(^{,*}\)
\(^{1}\) Department of Science and Technology, Rajarshi Janak University, Janakpurdham, Nepal
\(^{2}\) Department of Mathematics, G. G. V., Bilaspur, India
\(^{3}\) Department of Mathematics, Dr. C. V. Raman University, India
\(^{4}\) Department of Mathematics, NIT, Uttarakhand, Srinagar (Garhwal), India

Copyright © 2024 Suresh Kumar Sahani, A.K. Thakur, Avinash Kumar and K. Sharma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: June 18, 2023 – Accepted: February 2, 2024 – Published: May 15, 2024

Abstract

This study introduces theorems concerning matrix products, which delineate the transformations of sequences or series into other sequences or series, ensuring either the preservation of limits or the guarantee of convergence. Previous literature has explored the properties of matrices facilitating transformations between sequences, series, and their combinations, with detailed insights available in references [1,2,3].

Keywords:

Infinite series; matrices; convergence; sequence-to-sequence
]]> Some new results on w Up-algebras https://old.pisrt.org/psr-press/journals/oms-vol-8-2024/some-new-results-on-w-up-algebras/ Wed, 15 May 2024 15:53:37 +0000 https://old.pisrt.org/?p=8308
OMS-Vol. 8 (2024), Issue 1, pp. 8-16 Open Access Full-Text PDF
Daniel A. Romano
Abstract:The concept of weak UP-algebras (shortly wUP-algebra) is an extension of the notion of UP-algebras introduced in 2021 by Iampan and Romano. In this report, an effective extension of a (weak) UP-algebra to a wUP-algebra is created. In addition to the previous one, the concept of atoms in wUP-algebras is introduced and their important properties are registered. Finally, the concept of wUP-filters in wUP-algebras was introduced and its connections with other substructures in wUP-algebras were analyzed.]]>
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Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 8-16
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2024.0220

Some new results on w Up-algebras

Daniel A. Romano\(^{1,*}\)
\(^{1}\) International Mathematical Virtual Institute \newline Korduna\v ska Street 6, 78000 Banja Luka, Bosnia and Herzegovina; danielromano1949@gmail.com.

Copyright © 2024 Daniel A. Romano. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: August 25, 2023 – Accepted: April 6, 2024 – Published: May 15, 2024

Abstract

The concept of weak UP-algebras (shortly wUP-algebra) is an extension of the notion of UP-algebras introduced in 2021 by Iampan and Romano. In this report, an effective extension of a (weak) UP-algebra to a wUP-algebra is created. In addition to the previous one, the concept of atoms in wUP-algebras is introduced and their important properties are registered. Finally, the concept of wUP-filters in wUP-algebras was introduced and its connections with other substructures in wUP-algebras were analyzed.

Keywords:

UP-algebra, weak UP-algebra (shortly wUP-algebra), extension of a (weak) UP-algebra to a wUP-algebra, atoms in wUP-algebras, wUP-filters
]]> The skew constant and orthogonalities in Banach spaces https://old.pisrt.org/psr-press/journals/oms-vol-8-2024/the-skew-constant-and-orthogonalities-in-banach-spaces/ Wed, 15 May 2024 15:48:42 +0000 https://old.pisrt.org/?p=8306
OMS-Vol. 8 (2024), Issue 1, pp. 1-7 Open Access Full-Text PDF
Yin Zhou, Qichuan Ni and Qi Liu
Abstract:In normed spaces, Birkhoff orthogonality and isosceles orthogonality can be used to characterize space structures, and many scholars have introduced geometric constants to quantitatively describe the relationship between these two types of orthogonality. This paper introduces a new orthogonal relationship - Skew orthogonality - and proposes a new geometric constant to measure the "distance" of difference between skew orthogonality and Birkhoff orthogonality in normed spaces. In the end, we provide some examples of specific spaces.]]>
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Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 1-7
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2024.0219

The skew constant and orthogonalities in Banach spaces

Yin Zhou\(^{1}\) , Qichuan Ni\(^{1,*}\) , Qi Liu\(^{1}\)
\(^{1}\) School of Mathematics and Physics, Anqing Normal University, Anqing 246133, P. R. China; niqichuan111@163.com.

Copyright © 2024 Yin Zhou, Qichuan Ni and Qi Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: August 18, 2023 – Accepted: February 12, 2024 – Published: May 15, 2024

Abstract

In normed spaces, Birkhoff orthogonality and isosceles orthogonality can be used to characterize space structures, and many scholars have introduced geometric constants to quantitatively describe the relationship between these two types of orthogonality. This paper introduces a new orthogonal relationship – Skew orthogonality – and proposes a new geometric constant to measure the “distance” of difference between skew orthogonality and Birkhoff orthogonality in normed spaces. In the end, we provide some examples of specific spaces.

Keywords:

Birkhoff orthogonality; geometric constant; Hilbert spaces; uniformly non-square
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