International Journal of Mathematics and Mathematical Sciences最新文献

{"title":"Planar Graphs without Cycles of Length 3, 4, and 6 are (3, 3)-Colorable","authors":"Pongpat Sittitrai, W. Pimpasalee","doi":"10.1155/2024/7884281","DOIUrl":"https://doi.org/10.1155/2024/7884281","url":null,"abstract":"<jats:p>For non-negative integers <jats:inline-formula><a:math xmlns:a=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><a:msub><a:mrow><a:mi>d</a:mi></a:mrow><a:mrow><a:mn>1</a:mn></a:mrow></a:msub></a:math></jats:inline-formula> and <jats:inline-formula><c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"><c:msub><c:mrow><c:mi>d</c:mi></c:mrow><c:mrow><c:mn>2</c:mn></c:mrow></c:msub></c:math></jats:inline-formula>, if <jats:inline-formula><e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\"><e:msub><e:mrow><e:mi>V</e:mi></e:mrow><e:mrow><e:mn>1</e:mn></e:mrow></e:msub></e:math></jats:inline-formula> and <jats:inline-formula><g:math xmlns:g=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\"><g:msub><g:mrow><g:mi>V</g:mi></g:mrow><g:mrow><g:mn>2</g:mn></g:mrow></g:msub></g:math></jats:inline-formula> are two partitions of a graph <jats:inline-formula><i:math xmlns:i=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\"><i:mi>G</i:mi></i:math></jats:inline-formula>’s vertex set <jats:inline-formula><k:math xmlns:k=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\"><k:mi>V</k:mi><k:mfenced open=\"(\" close=\")\" separators=\"|\"><k:mrow><k:mi>G</k:mi></k:mrow></k:mfenced></k:math></jats:inline-formula>, such that <jats:inline-formula><p:math xmlns:p=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\"><p:msub><p:mrow><p:mi>V</p:mi></p:mrow><p:mrow><p:mn>1</p:mn></p:mrow></p:msub></p:math></jats:inline-formula> and <jats:inline-formula><r:math xmlns:r=\"http://www.w3.org/1998/Math/MathML\" id=\"M8\"><r:msub><r:mrow><r:mi>V</r:mi></r:mrow><r:mrow><r:mn>2</r:mn></r:mrow></r:msub></r:math></jats:inline-formula> induce two subgraphs of <jats:inline-formula><t:math xmlns:t=\"http://www.w3.org/1998/Math/MathML\" id=\"M9\"><t:mi>G</t:mi></t:math></jats:inline-formula>, called <jats:inline-formula><v:math xmlns:v=\"http://www.w3.org/1998/Math/MathML\" id=\"M10\"><v:mi>G</v:mi><v:mfenced open=\"[\" close=\"]\" separators=\"|\"><v:mrow><v:msub><v:mrow><v:mi>V</v:mi></v:mrow><v:mrow><v:mn>1</v:mn></v:mrow></v:msub></v:mrow></v:mfenced></v:math></jats:inline-formula> with maximum degree at most <jats:inline-formula><ab:math xmlns:ab=\"http://www.w3.org/1998/Math/MathML\" id=\"M11\"><ab:msub><ab:mrow><ab:mi>d</ab:mi></ab:mrow><ab:mrow><ab:mn>1</ab:mn></ab:mrow></ab:msub></ab:math></jats:inline-formula> and <jats:inline-formula><cb:math xmlns:cb=\"http://www.w3.org/1998/Math/MathML\" id=\"M12\"><cb:mi>G</cb:mi><cb:mfenced open=\"[\" close=\"]\" separators=\"|\"><cb:mrow><cb:msub><cb:mrow><cb:mi>V</cb:mi></cb:mrow><cb:mrow><cb:mn>2</cb:mn></cb:mrow></cb:msub></cb:mrow></cb:mfenced></cb:math></jats:inline-formula> with maximum degree at most <jats:inline-formula><hb:math xmlns:hb=\"http://www.w3.org/1998/Math/MathML\" id=\"M13\"><hb:msub><hb:mrow><hb:mi>d</hb:mi></hb:mrow><hb:mrow><hb:mn>2</hb:mn></hb:mrow></hb:msub></hb:math></jats:inline-formula>, respectively, then the graph <jats:inline-formula><jb:math xmlns:jb=\"http://www.w3.org/1998/Math/MathML\" id=\"M14\"><jb:mi>G</jb:mi></jb:math></jats:inline-formula> is said to be","PeriodicalId":509297,"journal":{"name":"International Journal of Mathematics and Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140996781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling the Impact of Air Pollution and Meteorological Variables on COVID-19 Transmission in Western Cape, South Africa","authors":"John Kamwele Mutinda, A. Langat","doi":"10.1155/2024/1591016","DOIUrl":"https://doi.org/10.1155/2024/1591016","url":null,"abstract":"Understanding the factors that influence COVID-19 transmission is essential in assessing and mitigating the spread of the pandemic. This study focuses on modeling the impact of air pollution and meteorological parameters on the risk of COVID-19 transmission in Western Cape Province, South Africa. The data used in this study consist of air pollution parameters, meteorological variables, and COVID-19 incidence observed for 262 days from April 26, 2020, to January 12, 2021. Lagged data were prepared for modeling based on a 6-day incubation period for COVID-19 disease. Based on the overdispersion property of the incidence, negative binomial (NB) and generalised Poisson (GP) regression models were fitted. Stepwise regression was used to select the significant predictors in both models based on the Akaike information criterion (AIC). The residuals of both NB and GB regression models were autocorrelated. An autoregressive integrated moving average (ARIMA) model was fitted to the residuals of both models. ARIMA (7, 1, 5) was fitted to the residuals of the NB model while ARIMA (1, 1, 6) was fitted for the residuals of the GP model. NB + ARIMA (7, 1, 5) and GP + ARIMA (1, 1, 6) models were tested for performance using root mean square error (RSME). GP + ARIMA (1, 1, 6) was selected as the optimal model. The results from the optimal model suggest that minimum temperature, ambient relative humidity, ambient wind speed, PM2.5, and NO2 at various lags are positively associated with COVID-19 incidence while maximum relative humidity, minimum relative humidity, solar radiation, maximum temperature, NO, PM load, PM10, SO2, and NOX at various lags have a negative association with COVID-19 incidence. Ambient wind direction and temperature showed a nonsignificant association with COVID-19 at all lags. This study suggests that meteorological and pollution parameters play a vital independent role in the transmission of the SARS-CoV-2 virus.","PeriodicalId":509297,"journal":{"name":"International Journal of Mathematics and Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140664551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Almost Existentially Closed Models in Positive Logic","authors":"Mohammed Belkasmi","doi":"10.1155/2024/5595281","DOIUrl":"https://doi.org/10.1155/2024/5595281","url":null,"abstract":"This paper explores the concept of almost positively closed models in the framework of positive logic. To accomplish this, we initially define various forms of the positive amalgamation property, such as h-amalgamation and symmetric and asymmetric amalgamation properties. Subsequently, we introduce certain structures that enjoy these properties. Following this, we introduce the concepts of Δ-almost positively closed and Δ-weekly almost positively closed. The classes of these structures contain and exhibit properties that closely resemble those of positive existentially closed models. In order to investigate the relationship between positive almost closed and positive strong amalgamation properties, we first introduce the sets of positive algebraic formulas ET and AlgT and the properties of positive strong amalgamation. We then show that if a model A of a theory T is a ET+A-weekly almost positively closed, then A is a positive strong amalgamation basis of T, and if A is a positive strong amalgamation basis of T, then A is AlT+A-weekly almost positively closed.","PeriodicalId":509297,"journal":{"name":"International Journal of Mathematics and Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140695902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis of COVID-19 Disease Model: Backward Bifurcation and Impact of Pharmaceutical and Nonpharmaceutical Interventions","authors":"Ibad Ullah, Nigar Ali, I. Haq, Imtiaz Ahmad, M. D. Albalwi, Md. Haider Ali Biswas","doi":"10.1155/2024/6069996","DOIUrl":"https://doi.org/10.1155/2024/6069996","url":null,"abstract":"The SEIQHR model, introduced in this study, serves as a valuable tool for anticipating the emergence of various infectious diseases, such as COVID-19 and illnesses transmitted by insects. An analysis of the model’s qualitative features was conducted, encompassing the computation of the fundamental reproduction number, R0. It was observed that the disease-free equilibrium point remains singular and locally asymptotically stable when R0<1, while the endemic equilibrium point exhibits uniqueness when R0>1. Additionally, specific conditions were outlined to guarantee the local asymptotic stability of both equilibrium points. Employing numerical simulations, the graphical representation illustrated the influence of model parameters on disease dynamics and the potential for its eradication across different noninteger orders of the Caputo derivative. In essence, the adoption of a fractional epidemic model contributes to a deeper comprehension and enhanced biological insights into the dynamics of diseases.","PeriodicalId":509297,"journal":{"name":"International Journal of Mathematics and Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140739193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical Solution of Two-Dimensional Nonlinear Unsteady Advection-Diffusion-Reaction Equations with Variable Coefficients","authors":"Endalew Getnet Tsega","doi":"10.1155/2024/5541066","DOIUrl":"https://doi.org/10.1155/2024/5541066","url":null,"abstract":"The advection-diffusion-reaction (ADR) equation is a fundamental mathematical model used to describe various processes in many different areas of science and engineering. Due to wide applicability of the ADR equation, finding accurate solution is very important to better understand a physical phenomenon represented by the equation. In this study, a numerical scheme for solving two-dimensional unsteady ADR equations with spatially varying velocity and diffusion coefficients is presented. The equations include nonlinear reaction terms. To discretize the ADR equations, the Crank–Nicolson finite difference method is employed with a uniform grid. The resulting nonlinear system of equations is solved using Newton’s method. At each iteration of Newton’s method, the Gauss–Seidel iterative method with sparse matrix computation is utilized to solve the block tridiagonal system and obtain the error correction vector. The consistency and stability of the numerical scheme are investigated. MATLAB codes are developed to implement this combined numerical approach. The validation of the scheme is verified by solving a two-dimensional advection-diffusion equation without reaction term. Numerical tests are provided to show the good performances of the proposed numerical scheme in simulation of ADR problems. The numerical scheme gives accurate results. The obtained numerical solutions are presented graphically. The result of this study may provide insights to apply numerical methods in solving comprehensive models of physical phenomena that capture the underlying situations.","PeriodicalId":509297,"journal":{"name":"International Journal of Mathematics and Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140360386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rings in Which Every Element Is a Sum of a Nilpotent and Three 7-Potents","authors":"Yanyuan Wang, Xinsong Yang","doi":"10.1155/2024/4402496","DOIUrl":"https://doi.org/10.1155/2024/4402496","url":null,"abstract":"<jats:p>In this article, we define and discuss strongly <jats:inline-formula><math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn><mo>,</mo><mn>7</mn></mrow></msub></math></jats:inline-formula> nil-clean rings: every element in a ring is the sum of a nilpotent and three 7-potents that commute with each other. We use the properties of nilpotent and 7-potent to conduct in-depth research and a large number of calculations and obtain a nilpotent formula for the constant <jats:inline-formula><math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"><mi>a</mi></math></jats:inline-formula>. Furthermore, we prove that a ring <jats:inline-formula><math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\"><mi>R</mi></math></jats:inline-formula> is a strongly <jats:inline-formula><math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\"><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn><mo>,</mo><mn>7</mn></mrow></msub></math></jats:inline-formula> nil-clean ring if and only if <jats:inline-formula><math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\"><mi>R</mi><mo>=</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>⊕</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⊕</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>⊕</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>⊕</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>⊕</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>6</mn></mrow></msub></math></jats:inline-formula>, where <jats:inline-formula><math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\"><msub><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msub></math></jats:inline-formula>, <jats:inline-formula><math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\"><msub><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msub></math></jats:inline-formula>, <jats:inline-formula><math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M8\"><msub><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msub></math></jats:inline-formula>, <jats:inline-formula><math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M9\"><msub><mrow><mi>R</mi></mrow><mrow><mn>4</mn></mrow></msub></math></jats:inline-formula>, <jats:inline-formula><math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M10\"><msub><mrow><mi>R</mi></mrow><mrow><mn>5</mn></mrow></msub></math></jats:inline-formula>, and <jats:inline-formula><math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M11\"><msub><mrow><mi>R</mi></mrow><mrow><mn>6</mn></mrow></msub></math></jats:inline-formula> are strongly <jats:inline-formula><math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M12\"><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn><mo>,</mo><mn>7</mn></mrow></msub></math></jats:inline-formula> nil-clean rings with <jats:inline-formula><math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M13\"><mn>2</mn><mo>∈</mo><mtext>Nil</mtext><mfenced open=\"(\" close=\")\" separators=\"|\"><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn","PeriodicalId":509297,"journal":{"name":"International Journal of Mathematics and Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140228142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New Weighted Burr XII Distribution: Statistical Properties, Applications, and Regression","authors":"Abdulzeid Yen Anafo, S. Ocloo, Suleman Nasiru","doi":"10.1155/2024/4098771","DOIUrl":"https://doi.org/10.1155/2024/4098771","url":null,"abstract":"In this study, a three-parameter modification of the Burr XII distribution has been developed through the integration of the weighted version of the alpha power transformation family of distributions. This newly introduced model, termed the modified alpha power-transformed Burr XII distribution, exhibits the unique ability to effectively model decreasing, right-skewed, or unimodal densities. The paper systematically elucidates various statistical properties of the proposed distribution. The estimation of parameters was obtained using maximum likelihood estimation. The estimator has been evaluated for consistency through simulation studies. To gauge the practical applicability of the proposed distribution, two distinct datasets have been employed. Comparative analyses involving six alternative distributions unequivocally demonstrate that the modified alpha power-transformed Burr XII distribution provides a better fit. Additionally, a noteworthy extension is introduced in the form of a location-scale regression model known as the log-modified alpha power-transformed Burr XII model. This model is subsequently applied to a dataset related to stock market liquidity. The findings underscore the enhanced fitting capabilities of the proposed model in comparison to existing distributions, providing valuable insights for applications in financial modelling and analysis.","PeriodicalId":509297,"journal":{"name":"International Journal of Mathematics and Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139848421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New Weighted Burr XII Distribution: Statistical Properties, Applications, and Regression","authors":"Abdulzeid Yen Anafo, S. Ocloo, Suleman Nasiru","doi":"10.1155/2024/4098771","DOIUrl":"https://doi.org/10.1155/2024/4098771","url":null,"abstract":"In this study, a three-parameter modification of the Burr XII distribution has been developed through the integration of the weighted version of the alpha power transformation family of distributions. This newly introduced model, termed the modified alpha power-transformed Burr XII distribution, exhibits the unique ability to effectively model decreasing, right-skewed, or unimodal densities. The paper systematically elucidates various statistical properties of the proposed distribution. The estimation of parameters was obtained using maximum likelihood estimation. The estimator has been evaluated for consistency through simulation studies. To gauge the practical applicability of the proposed distribution, two distinct datasets have been employed. Comparative analyses involving six alternative distributions unequivocally demonstrate that the modified alpha power-transformed Burr XII distribution provides a better fit. Additionally, a noteworthy extension is introduced in the form of a location-scale regression model known as the log-modified alpha power-transformed Burr XII model. This model is subsequently applied to a dataset related to stock market liquidity. The findings underscore the enhanced fitting capabilities of the proposed model in comparison to existing distributions, providing valuable insights for applications in financial modelling and analysis.","PeriodicalId":509297,"journal":{"name":"International Journal of Mathematics and Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139788802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"M-Polynomial and NM-Polynomial Methods for Topological Indices of Polymers","authors":"Mohammed Yasin H, M. Suresh, Z. G. Tefera, Samuel Asefa Fufa","doi":"10.1155/2024/1084450","DOIUrl":"https://doi.org/10.1155/2024/1084450","url":null,"abstract":"Topological indices (TIs) are numerical tools widely applied in chemometrics, biomedicine, and bioinformatics for predicting diverse physicochemical attributes and biological activities within molecular structures. Despite their significance, the challenges in deriving TIs necessitate novel approaches. This study addresses the limitations of conventional methods in dealing with dynamic molecular structures, focusing on the neighborhood M-polynomial (NM-polynomial), a pivotal polynomial for calculating degree-based TIs. Current literature acknowledges these polynomials but overlooks their limited adaptability to intricate biopolymer relationships. Our research advances by computing degree-based and neighborhood degree-based indices for prominent biopolymers, including polysaccharides, poly-γ-glutamic acid, and poly-L-lysine. Through innovative utilization of the NM-polynomial and the M-polynomial, we establish a fresh perspective on molecular structure and topological indices. Moreover, we present diverse graph representations highlighting the nuanced correlations between indices and structural parameters. By systematically investigating these indices and their underlying polynomials, our work contributes to predictive modelling in various fields. This exploration sheds light on intricate biochemical systems, offering insights into applications encompassing medicine, the food industry, and wastewater treatment. This research deepens our understanding of complex molecular interactions and paves the way for enhanced applications in diverse industries.","PeriodicalId":509297,"journal":{"name":"International Journal of Mathematics and Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139869157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"M-Polynomial and NM-Polynomial Methods for Topological Indices of Polymers","authors":"Mohammed Yasin H, M. Suresh, Z. G. Tefera, Samuel Asefa Fufa","doi":"10.1155/2024/1084450","DOIUrl":"https://doi.org/10.1155/2024/1084450","url":null,"abstract":"Topological indices (TIs) are numerical tools widely applied in chemometrics, biomedicine, and bioinformatics for predicting diverse physicochemical attributes and biological activities within molecular structures. Despite their significance, the challenges in deriving TIs necessitate novel approaches. This study addresses the limitations of conventional methods in dealing with dynamic molecular structures, focusing on the neighborhood M-polynomial (NM-polynomial), a pivotal polynomial for calculating degree-based TIs. Current literature acknowledges these polynomials but overlooks their limited adaptability to intricate biopolymer relationships. Our research advances by computing degree-based and neighborhood degree-based indices for prominent biopolymers, including polysaccharides, poly-γ-glutamic acid, and poly-L-lysine. Through innovative utilization of the NM-polynomial and the M-polynomial, we establish a fresh perspective on molecular structure and topological indices. Moreover, we present diverse graph representations highlighting the nuanced correlations between indices and structural parameters. By systematically investigating these indices and their underlying polynomials, our work contributes to predictive modelling in various fields. This exploration sheds light on intricate biochemical systems, offering insights into applications encompassing medicine, the food industry, and wastewater treatment. This research deepens our understanding of complex molecular interactions and paves the way for enhanced applications in diverse industries.","PeriodicalId":509297,"journal":{"name":"International Journal of Mathematics and Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139809199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}