In this paper, we take a new approach to uncertainty in a coherent system, where components are assumed to be all inactive in a given time. In particular, the signature-based method is used to quantify the extropy of the past lifetime of the system, which serves as a valuable indicator of its predictability. The results provide several key findings, including some bounds and stochastic ordering aspects for this measure. We also introduce a new formula to select the system that is preferable based on its relative extropy in the past. The results of this work can provide insights for designing systems to improve their reliability and resilience.
{"title":"System Level Extropy of the Past Life of a Coherent System","authors":"M. Kayid, Mashael A. Alshehri","doi":"10.1155/2023/9912509","DOIUrl":"https://doi.org/10.1155/2023/9912509","url":null,"abstract":"In this paper, we take a new approach to uncertainty in a coherent system, where components are assumed to be all inactive in a given time. In particular, the signature-based method is used to quantify the extropy of the past lifetime of the system, which serves as a valuable indicator of its predictability. The results provide several key findings, including some bounds and stochastic ordering aspects for this measure. We also introduce a new formula to select the system that is preferable based on its relative extropy in the past. The results of this work can provide insights for designing systems to improve their reliability and resilience.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"44 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89905345","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}
Linqiang Yang, Yafei Liu, Hongmei Ma, Xue Liu, Shuli Mei
The fractional population diffusion model is crucial for pest prevention. This paper presents an adaptive hierarchical collocation method for solving this model, enhancing the efficiency of algorithms based on Low-Complexity Shannon-Cosine wavelet derived from combinatorial identity theory. This function, an improvement over previous constructs, mitigates the need for iterative computation of parameters and boasts advantages like interpolation, symmetry, and compact support. The method’s extension to other time-fractional partial differential equations (PDEs) is also possible. The algorithm’s complexity analysis illustrates the concise function’s efficiency advantage over the original expression when solving time-fractional PDEs. Comparatively, the method exhibits superior numerical performance to alternative wavelet spectral methods like the Shannon–Gabor wavelet.
{"title":"Adaptive Hierarchical Collocation Method for Solving Fractional Population Diffusion Model","authors":"Linqiang Yang, Yafei Liu, Hongmei Ma, Xue Liu, Shuli Mei","doi":"10.1155/2023/2323418","DOIUrl":"https://doi.org/10.1155/2023/2323418","url":null,"abstract":"The fractional population diffusion model is crucial for pest prevention. This paper presents an adaptive hierarchical collocation method for solving this model, enhancing the efficiency of algorithms based on Low-Complexity Shannon-Cosine wavelet derived from combinatorial identity theory. This function, an improvement over previous constructs, mitigates the need for iterative computation of parameters and boasts advantages like interpolation, symmetry, and compact support. The method’s extension to other time-fractional partial differential equations (PDEs) is also possible. The algorithm’s complexity analysis illustrates the concise function’s efficiency advantage over the original expression when solving time-fractional PDEs. Comparatively, the method exhibits superior numerical performance to alternative wavelet spectral methods like the Shannon–Gabor wavelet.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"28 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85098087","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}
One of the requirements of curves in computer-aided design (CAD) is a curve with monotonic curvature profiles. Generalized log-aesthetic curves (GLACs) comprise a family of aesthetic curves which possesses a monotonic curvature profile. However, we cannot directly implement GLAC in CAD systems since it is in the form of a transcendental form. In this paper, we used cubic trigonometric Bézier (T-Bézier) curves with two shape parameters to approximate GLAC with G2 continuity. The final approximation formula inherits the shape parameters of GLAC whereas T-Béziers’ shape parameters are utilized to satisfy G2 constraints. Numerical results indicate that the proposed algorithm is capable of approximating GLAC within the given tolerance in (at least) two iterations.
{"title":"The Approximation of Generalized Log-Aesthetic Curves with <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <mrow>\u0000 ","authors":"Diya’ J. Albayari, R. Gobithaasan, K. Miura","doi":"10.1155/2023/7457223","DOIUrl":"https://doi.org/10.1155/2023/7457223","url":null,"abstract":"One of the requirements of curves in computer-aided design (CAD) is a curve with monotonic curvature profiles. Generalized log-aesthetic curves (GLACs) comprise a family of aesthetic curves which possesses a monotonic curvature profile. However, we cannot directly implement GLAC in CAD systems since it is in the form of a transcendental form. In this paper, we used cubic trigonometric Bézier (T-Bézier) curves with two shape parameters to approximate GLAC with G2 continuity. The final approximation formula inherits the shape parameters of GLAC whereas T-Béziers’ shape parameters are utilized to satisfy G2 constraints. Numerical results indicate that the proposed algorithm is capable of approximating GLAC within the given tolerance in (at least) two iterations.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"22 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88497870","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 paper, the marginal distribution of concomitants of k − record values (CKR) based on the Huang–Kotz Farlie–Gumbel–Morgenstern (HK-FGM) family of bivariate distributions is derived. In addition, we obtained the joint distribution of CKR for this family. Also, we obtained the hazard rate, reversed hazard rate, and residual life functions of CKR using the HK-FGM family. The weighted extropy and the weighted cumulative past extropy (WCPJ) are acquired for CKR under the HK-FGM family. In addition, we look into the issue of estimating the WCPJ by combining the empirical method with the concurrent use of KR in the HK-FGM family. Finally, we analyzed real-world data for illustration purposes, and the outcomes are rather striking.
{"title":"Weighted Extropy for Concomitants of Upper k-Record Values Based on Huang–Kotz Morgenstern of Bivariate Distribution","authors":"M. Nagy, Y. Tashkandy","doi":"10.1155/2023/3423690","DOIUrl":"https://doi.org/10.1155/2023/3423690","url":null,"abstract":"In this paper, the marginal distribution of concomitants of \u0000 \u0000 k\u0000 −\u0000 \u0000 record values (CKR) based on the Huang–Kotz Farlie–Gumbel–Morgenstern (HK-FGM) family of bivariate distributions is derived. In addition, we obtained the joint distribution of CKR for this family. Also, we obtained the hazard rate, reversed hazard rate, and residual life functions of CKR using the HK-FGM family. The weighted extropy and the weighted cumulative past extropy (WCPJ) are acquired for CKR under the HK-FGM family. In addition, we look into the issue of estimating the WCPJ by combining the empirical method with the concurrent use of KR in the HK-FGM family. Finally, we analyzed real-world data for illustration purposes, and the outcomes are rather striking.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"24 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74623327","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 paper, pointwise hemislant submanifolds were introduced in a Kahler manifold. The integrability conditions for the distributions which are involved in the definition of a pointwise hemislant submanifold were investigated. In addition, the necessary and sufficient conditions were given for a pointwise hemislant submanifold to be a pointwise hemislant product.
{"title":"Pointwise Hemislant Submanifolds in a Complex Space Form","authors":"Noura Alhouiti","doi":"10.1155/2023/8940238","DOIUrl":"https://doi.org/10.1155/2023/8940238","url":null,"abstract":"In this paper, pointwise hemislant submanifolds were introduced in a Kahler manifold. The integrability conditions for the distributions which are involved in the definition of a pointwise hemislant submanifold were investigated. In addition, the necessary and sufficient conditions were given for a pointwise hemislant submanifold to be a pointwise hemislant product.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"7 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83806807","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":"Global Existence and Decaying Rates of the Strong Solution for the Boussinesq System","authors":"Lu Wang, Shuokai Yan, Qinghua Zhang","doi":"10.1155/2023/6512823","DOIUrl":"https://doi.org/10.1155/2023/6512823","url":null,"abstract":"<jats:p>This paper focuses on the global existence and time-decay rates of the strong solution for the Boussinesq system with full viscosity in <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <msup>\u0000 <mrow>\u0000 <mi mathvariant=\"double-struck\">R</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula> for <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>n</mi>\u0000 <mo>≥</mo>\u0000 <mn>3</mn>\u0000 </math>\u0000 </jats:inline-formula>. Under the initial assumption of <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>θ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>u</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>/</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>×</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula> with a small norm, and <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <mi>n</mi>\u0000 <mo>></mo>\u0000 <mn>3</mn>\u0000 </math>\u0000 </jats:inline-formula","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"138 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74267805","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}
E. M. Eldemery, A. M. Abd-Elfattah, K. M. Mahfouz, Mohammed M. El Genidy
This paper investigates the estimation of an unknown shape parameter of the generalized Rayleigh distribution using Bayesian and expected Bayesian estimation techniques based on type-II censoring data. Subsequently, these estimators are obtained using four different loss functions: the linear exponential loss function, the weighted linear exponential loss function, the compound linear exponential loss function, and the weighted compound linear exponential loss function. The weighted compound linear exponential loss function is a novel suggested loss function generated by combining weights with the compound linear exponential loss function. We use the gamma distribution as a prior distribution. In addition, the expected Bayesian estimator is obtained through three different prior distributions of the hyperparameters. Moreover, depending on the four distinct forms of loss functions, Bayesian and expected Bayesian estimation techniques are performed using Monte Carlo simulations to verify the effectiveness of the suggested loss function and to compare Bayesian and expected Bayesian estimation methods. Furthermore, the simulation results indicate that, depending on the minimum mean squared error, the Bayesian and expected Bayesian estimations corresponding to the weighted compound linear exponential loss function suggested in this paper have significantly better performance compared to other loss functions, and the expected Bayesian estimator also performs better than the Bayesian estimator. Finally, the proposed techniques are demonstrated using a set of real data from the medical field to clarify the applicability of the suggested estimators to real phenomena and to show that the discussed weighted compound linear exponential loss function is efficient and can be applied in a real-life scenario.
{"title":"Bayesian and E-Bayesian Estimation for the Generalized Rayleigh Distribution under Different Forms of Loss Functions with Real Data Application","authors":"E. M. Eldemery, A. M. Abd-Elfattah, K. M. Mahfouz, Mohammed M. El Genidy","doi":"10.1155/2023/5454851","DOIUrl":"https://doi.org/10.1155/2023/5454851","url":null,"abstract":"This paper investigates the estimation of an unknown shape parameter of the generalized Rayleigh distribution using Bayesian and expected Bayesian estimation techniques based on type-II censoring data. Subsequently, these estimators are obtained using four different loss functions: the linear exponential loss function, the weighted linear exponential loss function, the compound linear exponential loss function, and the weighted compound linear exponential loss function. The weighted compound linear exponential loss function is a novel suggested loss function generated by combining weights with the compound linear exponential loss function. We use the gamma distribution as a prior distribution. In addition, the expected Bayesian estimator is obtained through three different prior distributions of the hyperparameters. Moreover, depending on the four distinct forms of loss functions, Bayesian and expected Bayesian estimation techniques are performed using Monte Carlo simulations to verify the effectiveness of the suggested loss function and to compare Bayesian and expected Bayesian estimation methods. Furthermore, the simulation results indicate that, depending on the minimum mean squared error, the Bayesian and expected Bayesian estimations corresponding to the weighted compound linear exponential loss function suggested in this paper have significantly better performance compared to other loss functions, and the expected Bayesian estimator also performs better than the Bayesian estimator. Finally, the proposed techniques are demonstrated using a set of real data from the medical field to clarify the applicability of the suggested estimators to real phenomena and to show that the discussed weighted compound linear exponential loss function is efficient and can be applied in a real-life scenario.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"80 6 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89430539","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}
<jats:p>In this paper, we are concerned with two points. First, the existence and uniqueness of the iterative fractional differential equation <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msup> <mrow /> <mrow> <mi>c</mi> </mrow> </msup> <msup> <mrow> <mi>D</mi> </mrow> <mrow> <mi>α</mi> </mrow> </msup> <mi>c</mi> <mi>x</mi> <mfenced open="(" close=")" separators="|"> <mrow> <mi>t</mi> </mrow> </mfenced> <mo>=</mo> <mi>f</mi> <mfenced open="(" close=")" separators="|"> <mrow> <mi>t</mi> <mo>,</mo> <mi>x</mi> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi>t</mi> </mrow> </mfenced> </mrow> <mo>,</mo> <mi>x</mi> <mfenced open="(" close=")" separators="|"> <mrow> <mi>g</mi> <mfenced open="(" close=")" separators="|"> <mrow> <mi>x</mi> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi>t</mi> </mrow> </mfenced> </mrow> </mrow> </mfenced> </mrow> </mfenced> </mrow> </mfenced> </math> </jats:inline-formula> are presented using the fixed-point theorem by imposing some conditions on <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2">
在本文中，我们关注两点。首先,迭代分数阶微分方程c D α的存在唯一性C x t = f t，xt，X g X t用不动点定理通过对f和g .其次，提出收敛于不动点的迭代方案。证明了该迭代方案的收敛性，并与所提出的迭代方案进行了比较。我们准备了算法来实现所提出的迭代方案。通过对不同α值的例子，我们成功地将所提出的迭代格式应用于给定的迭代微分方程。
{"title":"On Solutions to Fractional Iterative Differential Equations with Caputo Derivative","authors":"Alemnew Abera, Benyam Mebrate","doi":"10.1155/2023/5598990","DOIUrl":"https://doi.org/10.1155/2023/5598990","url":null,"abstract":"<jats:p>In this paper, we are concerned with two points. First, the existence and uniqueness of the iterative fractional differential equation <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <msup>\u0000 <mrow />\u0000 <mrow>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 </msup>\u0000 <msup>\u0000 <mrow>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mi>c</mi>\u0000 <mi>x</mi>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>=</mo>\u0000 <mi>f</mi>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>,</mo>\u0000 <mi>x</mi>\u0000 <mrow>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 <mo>,</mo>\u0000 <mi>x</mi>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>g</mi>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>x</mi>\u0000 <mrow>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> are presented using the fixed-point theorem by imposing some conditions on <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 ","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73136402","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：