<jats:p>In this study, a new sequence called the complex-type <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>k</mi> </math> </jats:inline-formula>-Pell number is defined. Also, we give properties of this sequence such as the generating matrix, the generating function, the combinatorial representations, the exponential representation, the sums, the permanental and determinantal representations, and the Binet formula. Then, we determine the periods of the recurrence sequence according to the modulo <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"> <mi>υ</mi> </math> </jats:inline-formula> and produce cyclic groups with the help of the generating matrices of the sequence. We also get some findings about the ranks and periods of the complex-type <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M4"> <mi>k</mi> </math> </jats:inline-formula>-Pell sequence. Additionally, we create relations between the orders of the cyclic groups produced and the periods of the sequence. Then, this sequence is moved to groups and examined in detail in finite groups. As an application, we get the periods of the complex-type <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M5"> <mn>2</mn> </math> </jats:inline-formula>-Pell numbers in the polyhedral groups <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M6"> <mfenced open="(" close=")" separators="|"> <mrow> <mi>υ</mi> <mo>,</mo> <mn>2,2</mn> </mrow> </mfenced> </math> </jats:inline-formula>, <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M7"> <mfenced open="(" close=")" separators="|"> <mrow> <mn>2</mn> <mo>,</mo> <mi>υ</mi> <mo>,</mo> <mn>2</mn> </mrow> </mfenced> </math> </jats:inline-formula>, and <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M8"> <mfenced open="(" close=")" separators="|"> <mrow> <mn>2,2</mn>
{"title":"The Complex-Type <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mi>k</mi>\u0000 </math>-Pell Numbers and Their Applications","authors":"Yeşim Aküzüm","doi":"10.1155/2023/6631659","DOIUrl":"https://doi.org/10.1155/2023/6631659","url":null,"abstract":"<jats:p>In this study, a new sequence called the complex-type <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>k</mi>\u0000 </math>\u0000 </jats:inline-formula>-Pell number is defined. Also, we give properties of this sequence such as the generating matrix, the generating function, the combinatorial representations, the exponential representation, the sums, the permanental and determinantal representations, and the Binet formula. Then, we determine the periods of the recurrence sequence according to the modulo <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mi>υ</mi>\u0000 </math>\u0000 </jats:inline-formula> and produce cyclic groups with the help of the generating matrices of the sequence. We also get some findings about the ranks and periods of the complex-type <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <mi>k</mi>\u0000 </math>\u0000 </jats:inline-formula>-Pell sequence. Additionally, we create relations between the orders of the cyclic groups produced and the periods of the sequence. Then, this sequence is moved to groups and examined in detail in finite groups. As an application, we get the periods of the complex-type <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <mn>2</mn>\u0000 </math>\u0000 </jats:inline-formula>-Pell numbers in the polyhedral groups <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>υ</mi>\u0000 <mo>,</mo>\u0000 <mn>2,2</mn>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula>, <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\">\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mi>υ</mi>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula>, and <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M8\">\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mn>2,2</mn>\u0000 ","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"14 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88569352","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}
M. Alam, Ahteshamul Haque, A. Khan, Samir Kasim, Amjad Ali Pasha, Aasim Zafar, K. Irshad, A. Chaudhary, Md. Samsuzzaman, R. Azim
Solar energy is a significant, environment-friendly source of renewable energy. The solar absorber transforms solar radiation into heat energy as an effective green energy source. Therefore, increasing its absorbing capacity can improve a solar absorber’s effectiveness. This paper proposes a tungsten tantalum alloy with silicon dioxide (WTa-SiO2) ceramic layer-based solar absorber system with two different metasurfaces to enhance absorptivity and boost the solar absorber efficacy. The absorbance is also improved by adjusting the resonator thickness and material thickness, and the maximum visible light absorption is achieved by the suggested solar filter design. Moreover, Golden Eagle Optimization (GE)-based deep AlexNet algorithm is proposed for predicting the parameter variation and their effect on absorbance. The optimization technique is used to increase the effectiveness of the solar absorber by optimizing the design parameters. The features from the WTa-SiO2 design are extracted by the proposed Principal Component-Autoencoder (PC-AE) method. Experimental results show that the proposed system can effectively predict absorptivity with a reduced computational time. The proposed method demonstrates superior prediction performance with an absorption prediction efficiency of 99.8% compared to the existing methods. Thus, the proposed WTa-SiO2 metasurface-based solar absorber can be used for photovoltaic applications.
{"title":"Metasurface-Based Solar Absorption Prediction System Using Artificial Intelligence","authors":"M. Alam, Ahteshamul Haque, A. Khan, Samir Kasim, Amjad Ali Pasha, Aasim Zafar, K. Irshad, A. Chaudhary, Md. Samsuzzaman, R. Azim","doi":"10.1155/2023/9489270","DOIUrl":"https://doi.org/10.1155/2023/9489270","url":null,"abstract":"Solar energy is a significant, environment-friendly source of renewable energy. The solar absorber transforms solar radiation into heat energy as an effective green energy source. Therefore, increasing its absorbing capacity can improve a solar absorber’s effectiveness. This paper proposes a tungsten tantalum alloy with silicon dioxide (WTa-SiO2) ceramic layer-based solar absorber system with two different metasurfaces to enhance absorptivity and boost the solar absorber efficacy. The absorbance is also improved by adjusting the resonator thickness and material thickness, and the maximum visible light absorption is achieved by the suggested solar filter design. Moreover, Golden Eagle Optimization (GE)-based deep AlexNet algorithm is proposed for predicting the parameter variation and their effect on absorbance. The optimization technique is used to increase the effectiveness of the solar absorber by optimizing the design parameters. The features from the WTa-SiO2 design are extracted by the proposed Principal Component-Autoencoder (PC-AE) method. Experimental results show that the proposed system can effectively predict absorptivity with a reduced computational time. The proposed method demonstrates superior prediction performance with an absorption prediction efficiency of 99.8% compared to the existing methods. Thus, the proposed WTa-SiO2 metasurface-based solar absorber can be used for photovoltaic applications.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"59 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84383425","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 mathematical model of a kind of two-robot security system with an early warning function is studied. By using strongly continuous operator semigroup theory and Volterra integral equation theory, the properties of the semigroup of the system operator, the existence and uniqueness of nonnegative solution, and the well-posedness of solution are discussed, respectively. Under the assumption that the failure rate and repair rate of the system are constants, the equations of the robot system are transformed into an ordinary differential equation group, and then the instantaneous reliability and stable-state reliability of the system are obtained. The reliability and zero-state controllability of the system are proved. Finally, the numerical solution of the system model is obtained by using MATLAB mathematical software, and the corresponding numerical simulation diagram is given. The results show that the conclusions of numerical calculation and numerical simulation are in accordance with the results of reliability theory, thereby the reliability of the robot safety system is verified.
{"title":"Research on the Reliability of a Two-Robot Security System with Early Warning Function","authors":"Yuhong Cui, Youde Tao, Zongyang Li","doi":"10.1155/2023/3214866","DOIUrl":"https://doi.org/10.1155/2023/3214866","url":null,"abstract":"In this paper, the mathematical model of a kind of two-robot security system with an early warning function is studied. By using strongly continuous operator semigroup theory and Volterra integral equation theory, the properties of the semigroup of the system operator, the existence and uniqueness of nonnegative solution, and the well-posedness of solution are discussed, respectively. Under the assumption that the failure rate and repair rate of the system are constants, the equations of the robot system are transformed into an ordinary differential equation group, and then the instantaneous reliability and stable-state reliability of the system are obtained. The reliability and zero-state controllability of the system are proved. Finally, the numerical solution of the system model is obtained by using MATLAB mathematical software, and the corresponding numerical simulation diagram is given. The results show that the conclusions of numerical calculation and numerical simulation are in accordance with the results of reliability theory, thereby the reliability of the robot safety system is verified.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"43 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86466173","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":"Sums of One Prime Power and Four Prime Cubes in Short Intervals","authors":"Gen Li, Xianjiu Huang, Xiaoming Pan, Li Yang","doi":"10.1155/2023/3244257","DOIUrl":"https://doi.org/10.1155/2023/3244257","url":null,"abstract":"<jats:p>Let <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mi>k</mi>\u0000 <mo>⩾</mo>\u0000 <mn>1</mn>\u0000 </math>\u0000 </jats:inline-formula> be an integer. In this study, we derive an asymptotic formula for the average number of representations of integers <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>n</mi>\u0000 <mo>=</mo>\u0000 <msubsup>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </msubsup>\u0000 <mo>+</mo>\u0000 <msubsup>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 </msubsup>\u0000 <mo>+</mo>\u0000 <msubsup>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 </msubsup>\u0000 <mo>+</mo>\u0000 <msubsup>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 </msubsup>\u0000 <mo>+</mo>\u0000 <msubsup>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>5</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 </msubsup>\u0000 </math>\u0000 </jats:inline-formula> in short intervals, where <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <msub>\u0000 <mrow>\u0000 ","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"8 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85190676","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 manuscript, we define the class of -weakly -projective QTAG-modules for the infinite ordinal and provide its systematic study for the finite ordinal. Furthermore, we generalize this class to -projective modules and obtain some characterizations. We also study the -totally weak -projective modules under the formation of -bijections.
在这份手稿中，对于无穷序数α，我们定义了一类ω 1 -弱α -射影qtag -模并对有限序数进行了系统的研究。进一步，我们将这个类推广到ω。2 + n -投影模，得到了一些刻画。我们也研究了完全弱的ω。ω 1 -双射形成下的2 + n -射影模。
{"title":"On Generalizations of Projective QTAG-Modules","authors":"F. Sikander, Firdhousi Begam, Tanveer Fatima","doi":"10.1155/2023/3175455","DOIUrl":"https://doi.org/10.1155/2023/3175455","url":null,"abstract":"<jats:p>In this manuscript, we define the class of <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <msub>\u0000 <mrow>\u0000 <mi>ω</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 </math>\u0000 </jats:inline-formula>-weakly <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>α</mi>\u0000 </math>\u0000 </jats:inline-formula>-projective QTAG-modules for the infinite ordinal <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mi>α</mi>\u0000 </math>\u0000 </jats:inline-formula> and provide its systematic study for the finite ordinal. Furthermore, we generalize this class to <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>ω</mi>\u0000 <mo>.</mo>\u0000 <mn>2</mn>\u0000 <mo>+</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula>-projective modules and obtain some characterizations. We also study the <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <mi>ω</mi>\u0000 </math>\u0000 </jats:inline-formula>-totally weak <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>ω</mi>\u0000 <mo>.</mo>\u0000 <mn>2</mn>\u0000 <mo>+</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula>-projective modules under the formation of <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\">\u0000 <msub>\u0000 <mrow>\u0000 <mi>ω</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 </math>\u0000 </jats:inline-formula>-bijections.</jats:p>","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"28 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80365664","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 studies the variable selection of high-dimensional spatial autoregressive panel models with fixed effects in which a matrix transformation method is applied to eliminate the fixed effects. Then, a penalized quasi-maximum likelihood is developed for variable selection and parameter estimation in the transformed panel model. Under some regular conditions, the consistency and oracle properties of the proposed estimator are established. Some Monte-Carlo experiments and a real data analysis are conducted to examine the finite sample performance of the proposed variable selection procedure, showing that the proposed variable selection method works satisfactorily.
{"title":"Variable Selection of High-Dimensional Spatial Autoregressive Panel Models with Fixed Effects","authors":"Miaojie Xia, Yuqi Zhang, Ruiqin Tian","doi":"10.1155/2023/9837117","DOIUrl":"https://doi.org/10.1155/2023/9837117","url":null,"abstract":"This paper studies the variable selection of high-dimensional spatial autoregressive panel models with fixed effects in which a matrix transformation method is applied to eliminate the fixed effects. Then, a penalized quasi-maximum likelihood is developed for variable selection and parameter estimation in the transformed panel model. Under some regular conditions, the consistency and oracle properties of the proposed estimator are established. Some Monte-Carlo experiments and a real data analysis are conducted to examine the finite sample performance of the proposed variable selection procedure, showing that the proposed variable selection method works satisfactorily.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"15 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91291458","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}
T. Mouktonglang, K. Poochinapan, P. Varnakovida, R. Suparatulatorn, Sompop Moonchai
The main objective of this article is to propose two novel parallel methods for solving common variational inclusion and common fixed point problems in a real Hilbert space. Strong convergence theorems of both methods are established by allowing for some mild conditions. Moreover, numerical studies of the signal recovery problem consisting of various blurred filters demonstrate the computational behavior of the proposed methods and other existing methods.
{"title":"Convergence Analysis of Two Parallel Methods for Common Variational Inclusion Problems Involving Demicontractive Mappings","authors":"T. Mouktonglang, K. Poochinapan, P. Varnakovida, R. Suparatulatorn, Sompop Moonchai","doi":"10.1155/2023/1910411","DOIUrl":"https://doi.org/10.1155/2023/1910411","url":null,"abstract":"The main objective of this article is to propose two novel parallel methods for solving common variational inclusion and common fixed point problems in a real Hilbert space. Strong convergence theorems of both methods are established by allowing for some mild conditions. Moreover, numerical studies of the signal recovery problem consisting of various blurred filters demonstrate the computational behavior of the proposed methods and other existing methods.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"19 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81973265","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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