Pub Date : 2021-06-09DOI: 10.37394/23206.2021.20.30
R. Alotaibi, Y. Tripathi, S. Dey, H. Rezk
In this paper, inference upon stress-strength reliability is considered for unit-Weibull distributions with a common parameter under the assumption that data are observed using progressive type II censoring. We obtain di_erent estimators of system reliability using classical and Bayesian procedures. Asymptotic interval is constructed based on Fisher information matrix. Besides, boot-p and boot-t intervals are also obtained. We evaluate Bayes estimates using Lindley's technique and Metropolis-Hastings (MH) algorithm. The Bayes credible interval is evaluated using MH method. An unbiased estimator of this parametric function is also obtained under know common parameter case. Numerical simulations are performed to compare estimation methods. Finally, a data set is studied for illustration purposes.
{"title":"Estimation of Multicomponent Reliability Based on Progressively Type II Censored Data from Unit Weibull Distribution","authors":"R. Alotaibi, Y. Tripathi, S. Dey, H. Rezk","doi":"10.37394/23206.2021.20.30","DOIUrl":"https://doi.org/10.37394/23206.2021.20.30","url":null,"abstract":"In this paper, inference upon stress-strength reliability is considered for unit-Weibull distributions with a common parameter under the assumption that data are observed using progressive type II censoring. We obtain di_erent estimators of system reliability using classical and Bayesian procedures. Asymptotic interval is constructed based on Fisher information matrix. Besides, boot-p and boot-t intervals are also obtained. We evaluate Bayes estimates using Lindley's technique and Metropolis-Hastings (MH) algorithm. The Bayes credible interval is evaluated using MH method. An unbiased estimator of this parametric function is also obtained under know common parameter case. Numerical simulations are performed to compare estimation methods. Finally, a data set is studied for illustration purposes.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115912069","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}
Pub Date : 2021-06-02DOI: 10.37394/23206.2021.20.28
N. Assimakis, M. Adam
New closed forms are presented of the solutions of the continuous and discrete Lyapunov equations using the vech and veck operators. The proposed solutions are faster than the classical solutions derived using the vec operator. The solutions via veck operator are faster than the solutions via vech operator. Key-Words: continuous Lyapunov equation, discrete Lyapunov equation, vec, vech, veck operator Received: April 6, 2021. Revised: May 20, 2021. Accepted: May 28, 2021. Published: June 2, 2021.
{"title":"Closed Form Solutions of Lyapunov Equations Using the Vech and Veck Operators","authors":"N. Assimakis, M. Adam","doi":"10.37394/23206.2021.20.28","DOIUrl":"https://doi.org/10.37394/23206.2021.20.28","url":null,"abstract":"New closed forms are presented of the solutions of the continuous and discrete Lyapunov equations using the vech and veck operators. The proposed solutions are faster than the classical solutions derived using the vec operator. The solutions via veck operator are faster than the solutions via vech operator. Key-Words: continuous Lyapunov equation, discrete Lyapunov equation, vec, vech, veck operator Received: April 6, 2021. Revised: May 20, 2021. Accepted: May 28, 2021. Published: June 2, 2021.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132238777","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}
Pub Date : 2021-06-02DOI: 10.37394/23206.2021.20.29
Wipawee Tangjai, Chusak Chubthaisong
Let p be a prime number where p ≡ 2 (mod 3). In this work, we give a nonnegative integer solution for the Diophantine equation 3x+py = z2. If y = 0, then (p, x, y, z) = (p, 1, 0, 2) is the only solution of the equation for each prime number p. If y is not divisible by 4, then the equation has a unique solution (p, x, y, z) = (2, 0, 3, 3). In case that y is a positive integer that is not divisible by 4, we give a necessary condition for an existence of a solution and give a computational result for p < 1017. We also give a necessary condition for an existence of a solution for qx + py = z2 when p and q are distinct prime numbers.
{"title":"On the Diophantine equation 3^x+p^y=z^2 where p ≡ 2 (mod 3)","authors":"Wipawee Tangjai, Chusak Chubthaisong","doi":"10.37394/23206.2021.20.29","DOIUrl":"https://doi.org/10.37394/23206.2021.20.29","url":null,"abstract":"Let p be a prime number where p ≡ 2 (mod 3). In this work, we give a nonnegative integer solution for the Diophantine equation 3x+py = z2. If y = 0, then (p, x, y, z) = (p, 1, 0, 2) is the only solution of the equation for each prime number p. If y is not divisible by 4, then the equation has a unique solution (p, x, y, z) = (2, 0, 3, 3). In case that y is a positive integer that is not divisible by 4, we give a necessary condition for an existence of a solution and give a computational result for p < 1017. We also give a necessary condition for an existence of a solution for qx + py = z2 when p and q are distinct prime numbers.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132936193","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}
Pub Date : 2021-05-24DOI: 10.37394/23206.2021.20.27
Adirek Vajrapatkul
As the general objective of a representative government is to achieve in creating the economic conditions that support the wellbeing of citizen, it, thus, needs to design and implement its policies in an appropriated manner. Hence, to support the valuable information for designing and implementing such policies, this work is designed to gain that information by trying to identify the reactions of various variables to government policies. To meet this objective, this work proposed a simple close economy Dynamic stochastic general equilibrium (DSGE) model with the public goods in the household consumption bundle. Also, the usual shocks studied in the DSGE model were included in the reaction investigation process. The Bayesian technique is then employed to estimate the model parameters by using the quarterly detrended data of Thailand in the period of 2001 to 2019. The result showed the crowding-out effect driven by government spending. Also, the reactions of the major macroeconomic variables to each shock were consistent with some previous studies. Key-words: DSGE, Close Economy, monetary policy, fiscal policy, Bayesian Estimation Received: March 15, 2021. Revised: May 10, 2021. Accepted: May 17, 2021. Published: May 24, 2021.
{"title":"The Shock Reaction in a Simple Close Economy","authors":"Adirek Vajrapatkul","doi":"10.37394/23206.2021.20.27","DOIUrl":"https://doi.org/10.37394/23206.2021.20.27","url":null,"abstract":"As the general objective of a representative government is to achieve in creating the economic conditions that support the wellbeing of citizen, it, thus, needs to design and implement its policies in an appropriated manner. Hence, to support the valuable information for designing and implementing such policies, this work is designed to gain that information by trying to identify the reactions of various variables to government policies. To meet this objective, this work proposed a simple close economy Dynamic stochastic general equilibrium (DSGE) model with the public goods in the household consumption bundle. Also, the usual shocks studied in the DSGE model were included in the reaction investigation process. The Bayesian technique is then employed to estimate the model parameters by using the quarterly detrended data of Thailand in the period of 2001 to 2019. The result showed the crowding-out effect driven by government spending. Also, the reactions of the major macroeconomic variables to each shock were consistent with some previous studies. Key-words: DSGE, Close Economy, monetary policy, fiscal policy, Bayesian Estimation Received: March 15, 2021. Revised: May 10, 2021. Accepted: May 17, 2021. Published: May 24, 2021.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133718734","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}
Pub Date : 2021-05-20DOI: 10.37394/23206.2021.20.26
A. Shatarah
in this paper, we investigated Toeplitz like operators on vector valued Hardy spaces. Toeplitz like operators on 2-nuclear tensor product of Hardy spaces are then constructed and described using the theory of p-nuclear tensor product of Banach spaces, and their basic algebraic properties and spectrum are analyzed. Key-Words: Toeplitz like operators , 2-nuclear tensor product of hardy spaces. Received: January 26, 2021. Revised: May 6, 2021. Accepted: May 14, 2021. Published: May 20, 2021.
{"title":"Toeplitz Like Operators on 2-nuclear Tensor Product of Hardy Spaces","authors":"A. Shatarah","doi":"10.37394/23206.2021.20.26","DOIUrl":"https://doi.org/10.37394/23206.2021.20.26","url":null,"abstract":"in this paper, we investigated Toeplitz like operators on vector valued Hardy spaces. Toeplitz like operators on 2-nuclear tensor product of Hardy spaces are then constructed and described using the theory of p-nuclear tensor product of Banach spaces, and their basic algebraic properties and spectrum are analyzed. Key-Words: Toeplitz like operators , 2-nuclear tensor product of hardy spaces. Received: January 26, 2021. Revised: May 6, 2021. Accepted: May 14, 2021. Published: May 20, 2021.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126715578","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}
Pub Date : 2021-05-19DOI: 10.37394/23206.2021.20.25
Adnan A. Y. Mustafa, Safat Kuwait
The task of data matching arises frequently in many aspects of science. It can become a time consuming process when the data is being matched to a huge database consisting of thousands of possible candidates, and the goal is to find the best match. It can be even more time consuming if the data are big (> 100 MB). One approach to reducing the time complexity of the matching process is to reduce the search space by introducing a pre-matching stage, where very dissimilar data are quickly removed. In this paper we focus our attention to matching big binary data. In this paper we present two probabilistic models for the quick dissimilarity detection of big binary data: the Probabilistic Model for Quick Dissimilarity Detection of Binary vectors (PMQDD) and the Inverse-equality Probabilistic Model for Quick Dissimilarity Detection of Binary vectors (IPMQDD). Dissimilarity detection between binary vectors can be accomplished quickly by random element mapping. The detection technique is not a function of data size and hence dissimilarity detection is performed quickly. We treat binary data as binary vectors, and hence any binary data of any size and dimension is treated as a binary vector. PMQDD is based on a binary similarity distance that does not recognize data and its exact inverse as containing the same pattern and hence considers them to be different. However, in some applications a specific data and its inverse, are regarded as the same pattern, and thus should be identified as being the same; IPMQDD is able to identify such cases, as it is based on a similarity distance that does not distinguish between data and its inverse instance as being dissimilar. We present a comparative analysis between PMQDD and IPMQDD, as well as their similarity distances. We present an application of the models to a set of object models, that show the effectiveness and power of these models.. Key-Words: Big data, binary data, binary vector, matching, size invariance, probabilistic model, dissimilarity detection, pattern recognition, model matching Received: March 27, 2021. Revised: April 30, 2021. Accepted: May 6, 2021. Published: May 19, 2021.
{"title":"Two Probabilistic Models for Quick Dissimilarity Detection of Big Binary Data","authors":"Adnan A. Y. Mustafa, Safat Kuwait","doi":"10.37394/23206.2021.20.25","DOIUrl":"https://doi.org/10.37394/23206.2021.20.25","url":null,"abstract":"The task of data matching arises frequently in many aspects of science. It can become a time consuming process when the data is being matched to a huge database consisting of thousands of possible candidates, and the goal is to find the best match. It can be even more time consuming if the data are big (> 100 MB). One approach to reducing the time complexity of the matching process is to reduce the search space by introducing a pre-matching stage, where very dissimilar data are quickly removed. In this paper we focus our attention to matching big binary data. In this paper we present two probabilistic models for the quick dissimilarity detection of big binary data: the Probabilistic Model for Quick Dissimilarity Detection of Binary vectors (PMQDD) and the Inverse-equality Probabilistic Model for Quick Dissimilarity Detection of Binary vectors (IPMQDD). Dissimilarity detection between binary vectors can be accomplished quickly by random element mapping. The detection technique is not a function of data size and hence dissimilarity detection is performed quickly. We treat binary data as binary vectors, and hence any binary data of any size and dimension is treated as a binary vector. PMQDD is based on a binary similarity distance that does not recognize data and its exact inverse as containing the same pattern and hence considers them to be different. However, in some applications a specific data and its inverse, are regarded as the same pattern, and thus should be identified as being the same; IPMQDD is able to identify such cases, as it is based on a similarity distance that does not distinguish between data and its inverse instance as being dissimilar. We present a comparative analysis between PMQDD and IPMQDD, as well as their similarity distances. We present an application of the models to a set of object models, that show the effectiveness and power of these models.. Key-Words: Big data, binary data, binary vector, matching, size invariance, probabilistic model, dissimilarity detection, pattern recognition, model matching Received: March 27, 2021. Revised: April 30, 2021. Accepted: May 6, 2021. Published: May 19, 2021.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131498061","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}
Pub Date : 2021-05-07DOI: 10.37394/23206.2021.20.24
R. Abdel-Baky, F. Mofarreh
For the curve on the regular surface, there is moving frame with this thatis named Darboux frame. Sweeping surfaces through the curve associated with Darboux frame are introduced and their geometrical properties are investigated. Moreover, we obtain the necessary and sufficient conditions of this kind of surfaces to be developable ruled surfaces. Finally, an example to illustrate the application of the results is introduced. Key-Words: Darboux frame, Sweeping surface, Singularity.
{"title":"Sweeping surface of center curve on surface in Euclidean 3-space E³","authors":"R. Abdel-Baky, F. Mofarreh","doi":"10.37394/23206.2021.20.24","DOIUrl":"https://doi.org/10.37394/23206.2021.20.24","url":null,"abstract":"For the curve on the regular surface, there is moving frame with this thatis named Darboux frame. Sweeping surfaces through the curve associated with Darboux frame are introduced and their geometrical properties are investigated. Moreover, we obtain the necessary and sufficient conditions of this kind of surfaces to be developable ruled surfaces. Finally, an example to illustrate the application of the results is introduced. Key-Words: Darboux frame, Sweeping surface, Singularity.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124715998","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}
Pub Date : 2021-05-04DOI: 10.37394/23206.2021.20.23
Faniran T. S.,, Bakare E. A.,, Potucek R.,, Ayoola E. O.
Covid-19 is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Many measures have been made by World Health Organization (WHO), but these may be threatened by unconcerned infectious individuals (some infectious individuals who do not take the disease serious, by ignoring non-pharmaceutical intervention). A system of nonlinear ordinary differential equations that absorbs a class of unconcerned infectious individuals, is developed. An invasion threshold parameter, Rc, is derived using the next generation matrix approach. This is used to establish the global stability of COVID-19-free equilibrium points. The global asymptotic stability of COVID-19 persistence equilibrium solution is studied through the use of suitable LaSalle’s Invariance Principle with a Lyapunov function of Goh-Volterra type. The intervention of themodel key parameters is assessed through sensitivity analysis. Our results indicate that increase in the rate of hospitalization of the asymptomatic infectious and unconcerned infectious individuals after a compulsory national testing, could bring Rc below one. Our results suggest that there should be compulsory national testing and continuous enhancement, the awareness through effective risk communication concerning COVID-19 to the general public. Numerical simulations are carried out to validate the analytical results. Key-Words: COVID-19, unconcerned infectious individuals, testing, stability analyses, sensitivity analysis Received: March 11, 2021. Revised: April 25, 2021. Accepted: April 30, 2021. Published: May 4, 2021.
{"title":"Global and Sensitivity Analyses of Unconcerned COVID-19 Cases in Nigeria: A Mathematical Modeling Approach","authors":"Faniran T. S.,, Bakare E. A.,, Potucek R.,, Ayoola E. O.","doi":"10.37394/23206.2021.20.23","DOIUrl":"https://doi.org/10.37394/23206.2021.20.23","url":null,"abstract":"Covid-19 is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Many measures have been made by World Health Organization (WHO), but these may be threatened by unconcerned infectious individuals (some infectious individuals who do not take the disease serious, by ignoring non-pharmaceutical intervention). A system of nonlinear ordinary differential equations that absorbs a class of unconcerned infectious individuals, is developed. An invasion threshold parameter, Rc, is derived using the next generation matrix approach. This is used to establish the global stability of COVID-19-free equilibrium points. The global asymptotic stability of COVID-19 persistence equilibrium solution is studied through the use of suitable LaSalle’s Invariance Principle with a Lyapunov function of Goh-Volterra type. The intervention of themodel key parameters is assessed through sensitivity analysis. Our results indicate that increase in the rate of hospitalization of the asymptomatic infectious and unconcerned infectious individuals after a compulsory national testing, could bring Rc below one. Our results suggest that there should be compulsory national testing and continuous enhancement, the awareness through effective risk communication concerning COVID-19 to the general public. Numerical simulations are carried out to validate the analytical results. Key-Words: COVID-19, unconcerned infectious individuals, testing, stability analyses, sensitivity analysis Received: March 11, 2021. Revised: April 25, 2021. Accepted: April 30, 2021. Published: May 4, 2021.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"1033 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123333266","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}
Pub Date : 2021-05-04DOI: 10.37394/23206.2021.20.22
M. Saad, A. Ansari, Muhammad Usman Akram, F. Alharbi
This paper aims to study spacelike surfaces from a given spacelike curve in Minkowski 3–space. Also, we investigate the necessary and sufficient conditions for the given space-like curve to be the line of curvature on the space-like surface. Depending on the causal character of the curve, the necessary and sufficient conditions for the given space-like curve to satisfy the line of curvature and the geodesic (resp. asymptotic) requirements are also analyzed. Furthermore, we give with illustration some computational examples in support of our main results.
{"title":"Spacelike Surfaces with a Common Line of Curvature in Lorentz-Minkowski 3-Space","authors":"M. Saad, A. Ansari, Muhammad Usman Akram, F. Alharbi","doi":"10.37394/23206.2021.20.22","DOIUrl":"https://doi.org/10.37394/23206.2021.20.22","url":null,"abstract":"This paper aims to study spacelike surfaces from a given spacelike curve in Minkowski 3–space. Also, we investigate the necessary and sufficient conditions for the given space-like curve to be the line of curvature on the space-like surface. Depending on the causal character of the curve, the necessary and sufficient conditions for the given space-like curve to satisfy the line of curvature and the geodesic (resp. asymptotic) requirements are also analyzed. Furthermore, we give with illustration some computational examples in support of our main results.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126182580","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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