For non-negative integers d1 and d2, if V1 and V2 are two partitions of a graph G’s vertex set VG, such that V1 and V2 induce two subgraphs of G, called GV1 with maximum degree at most d1 and GV2 with maximum degree at most d2, respectively, then the graph G is said to be
{"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}
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.
{"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}
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.
本文在正逻辑的框架内探讨了几乎正封闭模型的概念。为此，我们首先定义了正合属性的各种形式，如 h 合、对称和非对称合属性。随后，我们介绍了享有这些性质的某些结构。随后，我们引入了Δ-几乎正封闭和Δ-周几乎正封闭的概念。这些结构类包含并表现出与正存在封闭模型非常相似的性质。为了研究正几乎封闭与正强合并性质之间的关系，我们首先介绍了正代数式集 ET 和 AlgT 以及正强合并的性质。然后我们证明，如果一个理论 T 的模型 A 是 ET+A 周几乎正封闭，那么 A 就是 T 的正强合并基；如果 A 是 T 的正强合并基，那么 A 就是 AlT+A 周几乎正封闭。
{"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}
Ibad Ullah, Nigar Ali, I. Haq, Imtiaz Ahmad, M. D. Albalwi, Md. Haider Ali Biswas
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.
{"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}
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.
{"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}
In this article, we define and discuss strongly 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 . Furthermore, we prove that a ring is a strongly nil-clean ring if and only if , where , , , , , and are strongly nil-clean rings with
{"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}
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.
在本研究中，通过整合α幂变换系列分布的加权版本，对伯尔 XII 分布进行了三参数修正。这个新引入的模型被称为 "修正的阿尔法幂变换伯尔 XII 分布"，它展现了有效模拟递减、右斜或单峰密度的独特能力。论文系统地阐明了所提出的分布的各种统计特性。参数估计采用最大似然估计法。通过模拟研究对该估计方法的一致性进行了评估。为了评估所提出的分布的实际适用性，我们使用了两个不同的数据集。涉及六种替代分布的比较分析明确表明，修正的阿尔法幂变换伯尔 XII 分布具有更好的拟合效果。此外，还引入了一个值得注意的扩展，即位置尺度回归模型，即对数修正的阿尔法幂变换伯尔 XII 模型。该模型随后被应用于与股票市场流动性相关的数据集。研究结果表明，与现有分布相比，拟议模型的拟合能力更强，为金融建模和分析应用提供了宝贵的见解。
{"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}
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.
在本研究中，通过整合α幂变换系列分布的加权版本，对伯尔 XII 分布进行了三参数修正。这个新引入的模型被称为 "修正的阿尔法幂变换伯尔 XII 分布"，它展现了有效模拟递减、右斜或单峰密度的独特能力。论文系统地阐明了所提出的分布的各种统计特性。参数估计采用最大似然估计法。通过模拟研究对该估计方法的一致性进行了评估。为了评估所提出的分布的实际适用性，我们使用了两个不同的数据集。涉及六种替代分布的比较分析明确表明，修正的阿尔法幂变换伯尔 XII 分布具有更好的拟合效果。此外，还引入了一个值得注意的扩展，即位置尺度回归模型，即对数修正的阿尔法幂变换伯尔 XII 模型。该模型随后被应用于与股票市场流动性相关的数据集。研究结果表明，与现有分布相比，拟议模型的拟合能力更强，为金融建模和分析应用提供了宝贵的见解。
{"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}
Mohammed Yasin H, M. Suresh, Z. G. Tefera, Samuel Asefa Fufa
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.
拓扑指数（TIs）是广泛应用于化学计量学、生物医学和生物信息学的数值工具，用于预测分子结构中的各种物理化学属性和生物活性。尽管拓扑指数意义重大，但在推导拓扑指数时仍面临挑战，因此有必要采用新方法。本研究针对传统方法在处理动态分子结构时的局限性，重点研究了邻域 M 多项式（NM-polynomial），这是计算基于度数的 TI 的关键多项式。目前的文献承认这些多项式，但忽略了它们对错综复杂的生物聚合物关系的适应性有限。我们的研究通过计算主要生物聚合物（包括多糖、聚-γ-谷氨酸和聚-L-赖氨酸）的基于度和邻域度的指数取得了进展。通过对 NM 多项式和 M 多项式的创新利用，我们建立了分子结构和拓扑指数的全新视角。此外，我们还提出了多种图形表示法，突出了指数与结构参数之间的微妙关联。通过系统地研究这些指数及其底层多项式，我们的研究工作为各领域的预测建模做出了贡献。这一探索揭示了错综复杂的生化系统，为医学、食品工业和废水处理等应用领域提供了启示。这项研究加深了我们对复杂分子相互作用的理解，并为加强在不同行业的应用铺平了道路。
{"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}
Mohammed Yasin H, M. Suresh, Z. G. Tefera, Samuel Asefa Fufa
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.
拓扑指数（TIs）是广泛应用于化学计量学、生物医学和生物信息学的数值工具，用于预测分子结构中的各种物理化学属性和生物活性。尽管拓扑指数意义重大，但在推导拓扑指数时仍面临挑战，因此有必要采用新方法。本研究针对传统方法在处理动态分子结构时的局限性，重点研究了邻域 M 多项式（NM-polynomial），这是计算基于度数的 TI 的关键多项式。目前的文献承认这些多项式，但忽略了它们对错综复杂的生物聚合物关系的适应性有限。我们的研究通过计算主要生物聚合物（包括多糖、聚-γ-谷氨酸和聚-L-赖氨酸）的基于度和邻域度的指数取得了进展。通过对 NM 多项式和 M 多项式的创新利用，我们建立了分子结构和拓扑指数的全新视角。此外，我们还提出了多种图形表示法，突出了指数与结构参数之间的微妙关联。通过系统地研究这些指数及其底层多项式，我们的研究工作为各领域的预测建模做出了贡献。这一探索揭示了错综复杂的生化系统，为医学、食品工业和废水处理等应用领域提供了启示。这项研究加深了我们对复杂分子相互作用的理解，并为加强在不同行业的应用铺平了道路。
{"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}
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