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 robustness of the Olanrewaju-Olanrewaju regression kernel-based to nonparametric kernels for Support Vector Regressor (SVR) https://old.pisrt.org/psr-press/journals/easl-vol-7-issue-2-2024/on-the-robustness-of-the-olanrewaju-olanrewaju-regression-kernel-based-to-nonparametric-kernels-for-support-vector-regressor-svr/ Wed, 24 Jul 2024 15:09:55 +0000 https://old.pisrt.org/?p=8405
EASL-Vol. 7 (2024), Issue 2, pp. 42 - 54 Open Access Full-Text PDF
Rasaki Olawale Olanrewaju, Toyin Omoyeni Oguntola, Lukman Abiodun Nafiu and Sodiq Adejare Olanrewaju
Abstract:{In this article we studied and juxtaposed nonparametric Least Square and the Olanrewaju-Olanrewaju regression-type \({L_{(O - O){\lambda _{\gamma (\left| \theta \right|)}}}}\) kernels for supervised Support Vector Regressor (SVR) machine learning of hyperplane regression in a bivariate setting. The nonparametric kernels used to expound the SVR were Bisquare, Gaussian, Triweight, Uniform, Epanechnikov, and Triangular. Lagrangian multiplier estimation technique was adopted in estimating the involved SVR hyperplane regression coefficients as well as other embedded coefficients in each of the stated kernels. In addition, point estimate of the Euclidean distance (\(r\)) and error margin (\(d\)) in each of the SVR kernels were carved-out. In demonstration to the annual birthrate and its percentage change (\(\Delta \% \)) of the Nigeria populace from 1950 to 2023, the Olanrewaju-Olanrewaju regression-type kernel for SVR robustly outperformed the nonparametric and Least Square kernel-based SVRs with a miniature Cross-Validation index of -1205.49. 5.9% and 3.2% hyperplane estimated regression coefficients from the Olanrewaju-Olanrewaju kernel-based SVR were recorded for the annual birthrate and its percentage change (\(\Delta \% \)) respectively. Interpretably, this connotes that for every one percent increment in the annual birthrate per 1000, the mean rate of the Nigeria populace from 1950 to 2023 increased by 5.9% while other variables were held constant. Similarly, its percentage change per 1000 increased by 3.2% while other variables were held constant. In recommendation, the nonparametric and Olanrewaju-Olanrewaju regression-type SVRs as well as the Least Square SVR were pinpointed for future consideration of categorical, missing and zero bivariate observations. ]]>
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Engineering and Applied Science Letter
Vol. 7 (2024), Issue 1, pp. 42 – 54
ISSN: 2617-9709 (Online) 2617-9695 (Print)
DOI: 10.30538/psrp-easl2024.0101

On the robustness of the Olanrewaju-Olanrewaju regression kernel-based to nonparametric kernels for Support Vector Regressor (SVR)

Rasaki Olawale Olanrewaju\(^{1,*}\), Toyin Omoyeni Oguntola\(^{2}\), Lukman Abiodun Nafiu\(^{3}\) and Sodiq Adejare Olanrewaju\(^{4}\)
\(^{1}\) Business Analytics Value Networks (BAVNs), Africa Business School (ABS), Mohammed VI Polytechnic University (UM6P), X4JH+QJR Avenue Mohamed Ben Abdellah Regragui, Rabat 10112, Morocco
\(^{2}\) Ladoke Akintola University of Technology, Ogbomoso, Oyo State, Nigeria
\(^{3}\) School of Graduates and Research at Metropolitan International University (MIU), Kampala, Uganda
\(^{4}\) Department of Statistics, University of Ibadan, Ibadan, University of Ibadan, 900001, Oyo State, Nigeria

Copyright © 2024 Rasaki Olawale Olanrewaju, Toyin Omoyeni Oguntola, Lukman Abiodun Nafiu and Sodiq Adejare Olanrewaju. 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: May 01, 2024 – Accepted: June 12, 2024 – Published: June 30, 2024

Abstract

Rasaki Olawale Olanrewaju, Toyin Omoyeni Oguntola, Lukman Abiodun Nafiu and Sodiq Adejare Olanrewaju

Abstract:{In this article we studied and juxtaposed nonparametric Least Square and the Olanrewaju-Olanrewaju regression-type \({L_{(O – O){\lambda _{\gamma (\left| \theta \right|)}}}}\) kernels for supervised Support Vector Regressor (SVR) machine learning of hyperplane regression in a bivariate setting. The nonparametric kernels used to expound the SVR were Bisquare, Gaussian, Triweight, Uniform, Epanechnikov, and Triangular. Lagrangian multiplier estimation technique was adopted in estimating the involved SVR hyperplane regression coefficients as well as other embedded coefficients in each of the stated kernels. In addition, point estimate of the Euclidean distance (\(r\)) and error margin (\(d\)) in each of the SVR kernels were carved-out. In demonstration to the annual birthrate and its percentage change (\(\Delta \% \)) of the Nigeria populace from 1950 to 2023, the Olanrewaju-Olanrewaju regression-type kernel for SVR robustly outperformed the nonparametric and Least Square kernel-based SVRs with a miniature Cross-Validation index of -1205.49. 5.9% and 3.2% hyperplane estimated regression coefficients from the Olanrewaju-Olanrewaju kernel-based SVR were recorded for the annual birthrate and its percentage change (\(\Delta \% \)) respectively. Interpretably, this connotes that for every one percent increment in the annual birthrate per 1000, the mean rate of the Nigeria populace from 1950 to 2023 increased by 5.9% while other variables were held constant. Similarly, its percentage change per 1000 increased by 3.2% while other variables were held constant. In recommendation, the nonparametric and Olanrewaju-Olanrewaju regression-type SVRs as well as the Least Square SVR were pinpointed for future consideration of categorical, missing and zero bivariate observations.

Keywords:

Kernels, Lagrangian Multiplier, Least Square, Olanrewaju-Olanrewaju Regression-Type, Nonparametric Regression, Support Vector Regressor (SVR)
]]> Dose response Hill model for the arsenic contamination in the groundwater samples of the Lakhimpur district of Uttar Pradesh https://old.pisrt.org/psr-press/journals/easl-vol-7-issue-2-2024/dose-response-hill-model-for-the-arsenic-contamination-in-the-groundwater-samples-of-the-lakhimpur-district-of-uttar-pradesh/ Wed, 24 Jul 2024 14:50:11 +0000 https://old.pisrt.org/?p=8403
EASL-Vol. 7 (2024), Issue 2, pp. 29 – 41 Open Access Full-Text PDF
Sudhanshu Aggarwal and Lalit Mohan Upadhyaya
Abstract:An experimental study conducted by Ankit Kumar and colleagues (Kumar, Gupta, Pandey, Govil, and Patel, “Status of Arsenic Contamination in District Lakhimpur, Uttar Pradesh, India,” in Emerging Trends in Science, Social Science and Engineering, edited by Aggarwal, Pandey, Naik, Mishra, Raj, Tripathi, and Shukla, pp. 60-73, ISBN 9789358380125, Astitva Prakashan, Bilaspur, Chhattisgarh) has identified significant levels of arsenic contamination in the groundwater of Lakhimpur district, Uttar Pradesh. Their findings indicate that arsenic levels are notably higher in the shallow regions compared to the deeper India Mark II regions across eight selected study sites. Building on these findings, this paper aims to apply a dose-response Hill model to analyze and explain the observed patterns of arsenic contamination in the groundwater resources of Lakhimpur district. ]]>
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Engineering and Applied Science Letter
Vol. 7 (2024), Issue 2, pp. 29 – 41
ISSN: 2617-9709 (Online) 2617-9695 (Print)
DOI: 10.30538/psrp-easl2024.0100

Dose response Hill model for the arsenic contamination in the groundwater samples of the Lakhimpur district of Uttar Pradesh

Sudhanshu Aggarwal\(^{1}\) and Lalit Mohan Upadhyaya\(^2,*\)
\(^{1}\) Department of Mathematics, National Post Graduate College, Barhalganj, Gorakhpur, Uttar Pradesh -273402, India
\(^{2}\) Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun, Uttarakhand -248179, India

Copyright © 2024 Sudhanshu Aggarwal and Lalit Mohan Upadhyaya. 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 21, 2024 – Accepted: June 12, 2024 – Published: June 30, 2024

Abstract

An experimental study conducted by Ankit Kumar and colleagues (Kumar, Gupta, Pandey, Govil, and Patel, “Status of Arsenic Contamination in District Lakhimpur, Uttar Pradesh, India,” in Emerging Trends in Science, Social Science and Engineering, edited by Aggarwal, Pandey, Naik, Mishra, Raj, Tripathi, and Shukla, pp. 60-73, ISBN 9789358380125, Astitva Prakashan, Bilaspur, Chhattisgarh) has identified significant levels of arsenic contamination in the groundwater of Lakhimpur district, Uttar Pradesh. Their findings indicate that arsenic levels are notably higher in the shallow regions compared to the deeper India Mark II regions across eight selected study sites. Building on these findings, this paper aims to apply a dose-response Hill model to analyze and explain the observed patterns of arsenic contamination in the groundwater resources of Lakhimpur district.

Keywords:

arsenic; arsenic contamination; regression; DR Hill model; Hill slope; regression.
]]> Emerging trends of nanomaterials synthesis using bos taurus urine https://old.pisrt.org/psr-press/journals/easl-vol-7-issue-2-2024/emerging-trends-of-nanomaterials-synthesis-using-bos-taurus-urine/ Tue, 23 Jul 2024 16:31:19 +0000 https://old.pisrt.org/?p=8398
EASL-Vol. 7 (2024), Issue 2, pp. 14 – 28 Open Access Full-Text PDF
Sampada B. Warake, Prashant D Sarvalkar, Neeraj R. Prasad, Avinash A. Ramteke, Kiran K Sharma
Abstract:The ability of organisms or organic compounds to reduce metal ions and stabilize them into nanoparticles is known as green synthesis. Various synthesis methods have been developed, each with its own advantages and drawbacks. In recent years, nanomaterials have found extensive applications in biological sciences, particularly in health and veterinary medicine. For these applications, it is crucial that nanomaterials are biocompatible and non-toxic. Consequently, researchers have increasingly focused on biological synthesis routes. Drawing inspiration from the ancient Indian system of medicine, Ayurveda, some researchers have recently synthesized nanomaterials using Indian cow urine. This review aims to catalog the various nanomaterials produced using Indian cow urine and to discuss their catalytic and biological activities. ]]>
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Engineering and Applied Science Letter
Vol. 7 (2024), Issue 2, pp. 14 – 28
ISSN: 2617-9709 (Online) 2617-9695 (Print)
DOI: 10.30538/psrp-easl2024.0099

Exploring effective iterative methods for nonlinear equations by using variational iteration technique

Sampada B. Warake\(^{1}\), Prashant D Sarvalkar\(^{2}\), Neeraj R. Prasad\(^{2}\), Avinash A. Ramteke\(^{1,*}\), Kiran K Sharma\(^{2}\)
\(^{1}\) Department of Chemistry, Devchand College, Arjunnagar-591237, Dist. – Kolhapur, Maharashtra, India
\(^{2}\) Nanoscience and Technology, Shivaji University Kolhapur, India

Copyright © 2024 Sampada B. Warake, Prashant D Sarvalkar, Neeraj R. Prasad, Avinash A. Ramteke, Kiran 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: April 07, 2024 – Accepted: June 12, 2024 – Published: June 30, 2024

Abstract

The ability of organisms or organic compounds to reduce metal ions and stabilize them into nanoparticles is known as green synthesis. Various synthesis methods have been developed, each with its own advantages and drawbacks. In recent years, nanomaterials have found extensive applications in biological sciences, particularly in health and veterinary medicine. For these applications, it is crucial that nanomaterials are biocompatible and non-toxic. Consequently, researchers have increasingly focused on biological synthesis routes. Drawing inspiration from the ancient Indian system of medicine, Ayurveda, some researchers have recently synthesized nanomaterials using Indian cow urine. This review aims to catalog the various nanomaterials produced using Indian cow urine and to discuss their catalytic and biological activities.

Keywords:

Bos taurus urine, Bio-synthesis, Nanomaterials, Biological activity, Catalytic efficacy
]]> Mathematical algorithms for perpetual ethiopian calendar(e.c.)and similar calendars https://old.pisrt.org/psr-press/journals/easl-vol-7-issue-2-2024/mathematical-algorithms-for-perpetual-ethiopian-calendare-c-and-similar-calendars/ Tue, 23 Jul 2024 15:57:41 +0000 https://old.pisrt.org/?p=8393
EASL-Vol. 7 (2024), Issue 2, pp. 1 – 13 Open Access Full-Text PDF
Aschale Moges Belay and Snehashish Chakraverty
Abstract:This study focused on developing mathematical algorithms for the perpetual Ethiopian calendar and similar calendars. The primary objective was to demonstrate the methodology for creating these algorithms. The research identified that arithmetic progression, ceiling function, congruence modulo, floor function, and Bahre Hasabe are fundamental concepts necessary for this development. Utilizing these concepts, the study successfully developed mathematical algorithms for the perpetual Ethiopian calendar and analogous calendars. ]]>
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Engineering and Applied Science Letter
Vol. 7 (2024), Issue 2, pp. 1 – 13
ISSN: 2617-9709 (Online) 2617-9695 (Print)
DOI: 10.30538/psrp-easl2024.0098

Mathematical algorithms for perpetual Ethiopian calendar(e.c.)and similar calendars

Aschale Moges Belay\(^{1}\) and Snehashish Chakraverty\(^2,*\)
\(^{1}\) Department of Mathematics, Debark University, P.O.Box 90, Ethiopia
\(^{2}\) Department of Mathematics, NIT Rourkela, India

Copyright © 2024 Aschale Moges Belay and Snehashish Chakraverty. 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 24, 2024 – Accepted: June 22, 2024 – Published: June 30, 2024

Abstract

This study focused on developing mathematical algorithms for the perpetual Ethiopian calendar and similar calendars. The primary objective was to demonstrate the methodology for creating these algorithms. The research identified that arithmetic progression, ceiling function, congruence modulo, floor function, and Bahre Hasabe are fundamental concepts necessary for this development. Utilizing these concepts, the study successfully developed mathematical algorithms for the perpetual Ethiopian calendar and analogous calendars.

Keywords:

Arithmetic progression; Bahre Hasabe; Ceiling function; Congruence modulo; Ethiopian calendar; Fasting dates; Floor function; Holidays
]]> On edge irregularity strength of some classes of Toeplitz graphs https://old.pisrt.org/psr-press/journals/odam-vol-7-issue-2-2024/on-edge-irregularity-strength-of-some-classes-of-toeplitz-graphs/ Sun, 07 Jul 2024 11:50:16 +0000 https://old.pisrt.org/?p=8380
ODAM-Vol. 7 (2024), Issue 2, pp. 23 - 34 Open Access Full-Text PDF
Noha Mohammad Seyam, Muhammad Faisal Nadeem
Abstract:An edge irregular \(k\)-labeling of a graph \(G\) is a labeling of vertices of \(G\) with labels from the set \(\{1,2,3,\dots,k\}\) such that no two edges of \(G\) have same weight. The least value of \(k\) for which a graph \(G\) has an edge irregular \(k\)-labeling is called the edge irregularity strength of \(G\). Ahmad et. al. [1] showed the edge irregularity strength of some particular classes of Toeplitz graphs. In this paper we generalize those results and finds the exact values of the edge irregularity strength for some generalize classes of Toeplitz graphs. ]]>
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Open Journal of Discrete Applied Mathematics
Vol. 7 (2024), Issue 2, pp. 23-34
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2024.0100

On edge irregularity strength of some classes of Toeplitz graphs

Noha Mohammad Seyam\(^1,\) Muhammad Faisal Nadeem$^{2,*}$
\(^1\) College of Applied Sciences Mathematical Sciences Department, Umm Al-Qura University, Makkah Saudi Arabia; nmseyam@uqu.edu.sa
\(^2\) Department of Mathematics, COMSATS University Islamabad Lahore Campus, Lahore 54000 Pakistan; mfaisalnadeem@ymail.com

Copyright © 2024 Noha Mohammad Seyam, Muhammad Faisal Nadeem. 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: May 14, 2024 – Accepted: June 09, 2024 – Published: June 30, 2024

Abstract

An edge irregular \(k\)-labeling of a graph \(G\) is a labeling of vertices of \(G\) with labels from the set \(\{1,2,3,\dots,k\}\) such that no two edges of \(G\) have same weight. The least value of \(k\) for which a graph \(G\) has an edge irregular \(k\)-labeling is called the edge irregularity strength of \(G\). Ahmad et. al. [1] showed the edge irregularity strength of some particular classes of Toeplitz graphs. In this paper we generalize those results and finds the exact values of the edge irregularity strength for some generalize classes of Toeplitz graphs.

Keywords:

irregular assignment; irregularity strength; edge irregularity strength; Toeplitz graph
]]> On the eccentric atom-bond sum-connectivity index https://old.pisrt.org/psr-press/journals/odam-vol-7-issue-2-2024/on-the-eccentric-atom-bond-sum-connectivity-index/ Sun, 07 Jul 2024 11:47:47 +0000 https://old.pisrt.org/?p=8378
ODAM-Vol. 7 (2024), Issue 2, pp. 11 - 22 Open Access Full-Text PDF
Zaryab Hussain, Muhammad Ahsan Binyamin
Abstract:This note presents some upper bounds for the size of the upper deg-centric grapg \(G_{ud}\) of a simple connected graph G. Amongst others, a result for graphs for which a compliant graph \(G\) has \(G_{ud} \cong \overline G\) is presented. Finally, results for size minimality in respect upper deg-centrication and minimum size of such graph \(G\) are presented.]]>
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Open Journal of Discrete Applied Mathematics
Vol. 7 (2024), Issue 2, pp. 11 – 22
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2024.0099

On the eccentric atom-bond sum-connectivity index

Zaryab Hussain\(^{1,*}\), Muhammad Ahsan Binyamin\(^{2}\)
\(^{1}\) School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, Shaanxi 710129, China; zaryabhussain2139@gmail.com
\(^{2}\) Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan; ahsanbanyamin@gmail.com

Copyright © 2024 Zaryab Hussain, Muhammad Ahsan Binyamin. 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 9, 2024 – Accepted: June 29, 2024 – Published: June 30, 2024

Abstract

The eccentric atom-bond sum-connectivity \(\left(ABSC_{e}\right)\) index of a graph \(G\) is defined as \(ABSC_{e}(G)=\sum\limits_{uv\in E(G)}\sqrt{\frac{e_{u}+e_{v}-2}{e_{u}+e_{v}}}\), where \(e_{u}\) and \(e_{v}\) represent the eccentricities of \(u\) and \(v\) respectively. This work presents precise upper and lower bounds for the \(ABSC_{e}\) index of graphs based on their order, size, diameter, and radius. Moreover, we find the maximum and minimum \(ABSC_{e}\) index of trees based on the specified matching number and the number of pendent vertices.

Keywords:

eccentric atom-bond sum-connectivity index; tree; matching number; pendent vertex
]]> The inverse degree conditions for Hamiltonian and traceable graphs https://old.pisrt.org/psr-press/journals/odam-vol-7-issue-2-2024/the-inverse-degree-conditions-for-hamiltonian-and-traceable-graphs/ Sun, 07 Jul 2024 11:45:11 +0000 https://old.pisrt.org/?p=8376
ODAM-Vol. 7 (2024), Issue 2, pp. 7 - 10 Open Access Full-Text PDF
Rao Li
Abstract:Let \(G = (V(G), E(G))\) be a graph with minimum degree at least \(1\). The inverse degree of \(G\), denoted \(Id(G)\), is defined as the sum of the reciprocals of degrees of all vertices in \(G\). In this note, we present inverse degree conditions for Hamiltonian and traceable graphs. ]]>
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Open Journal of Discrete Applied Mathematics
Vol. 7 (2024), Issue 2, pp. 7 – 10
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2024.0098

The inverse degree conditions for Hamiltonian and traceable graphs

Rao Li\(^{1,*}\)
\(^{1}\)Dept. of Computer Science, Engineering, and Math University of South Carolina Aiken, Aiken, SC 29801; raol@usca.edu

Copyright © 2024 Rao Li. 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: May 10, 2024 – Accepted: June 09, 2024 – Published: June 30, 2024

Abstract

Let \(G = (V(G), E(G))\) be a graph with minimum degree at least \(1\). The inverse degree of \(G\), denoted \(Id(G)\), is defined as the sum of the reciprocals of degrees of all vertices in \(G\). In this note, we present inverse degree conditions for Hamiltonian and traceable graphs.

Keywords:

the inverse degree; Hamiltonian graph, traceable graph.
]]> A direct proof of stability of nonnegative weak solution for fractional \(\mathbf{p}\)-Laplacian problem with concave nonlinearity https://old.pisrt.org/psr-press/journals/oma-vol-8-issue-1-2024/a-direct-proof-of-stability-of-nonnegative-weak-solution-for-fractional-mathbfp-laplacian-problem-with-concave-nonlinearity/ Sat, 06 Jul 2024 15:03:18 +0000 https://old.pisrt.org/?p=8373
OMA-Vol. 8 (2024), Issue 1, pp. 76 - 79 Open Access Full-Text PDF
Salah A. Khafagy
Abstract: The present paper provides a direct proof of stability of nontrivial nonnegative weak solution for fractional \(p\)-Laplacian problem under concave nonlinearity condition. The main results of this work are extend the previously known results for the fractional Laplacian problem. ]]>
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Open Journal of Mathematical Analysis
Vol. 8 (2024), Issue 1, pp. 76 – 79
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2024.0136

A direct proof of stability of nonnegative weak solution for fractional \(\mathbf{p}\)-Laplacian problem with concave nonlinearity

Salah A. Khafagy\(^{1,*}\)
\(^{1}\) Department of Mathematics, Royal University of Phnom Penh, Phnom Penh, Cambodia.

Copyright © 2024 Salah A. Khafagy. 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 20, 2024 – Accepted: May 8, 2024 – Published: June 30, 2024

Abstract

The present paper provides a direct proof of stability of nontrivial nonnegative weak solution for fractional \(p\)-Laplacian problem under concave nonlinearity condition. The main results of this work are extend the previously known results for the fractional Laplacian problem.

Keywords:

Stability; weak solution; fractional \(p\)-Laplacian
]]>