In this paper, we first define the vector product in a special analog Minkowski Geometry $(mathbb{R}^3,langle,rangle) $ which is identified with the space of spatial hybrids. Next, we derive the Frenet-Serret frame formulae for a three dimensional non-parabolic curve by using the spatial hybrids and the vector product. However, we present the Frenet-Serret Frame formulae of a non-lightlike hybrid curve in $mathbb{R}^4$ and an illustrative example for all theorems of the paper with Matlab codes.
{"title":"ON HYBRID CURVES","authors":"Mücahit AKBIYIK","doi":"10.30931/jetas.1338660","DOIUrl":"https://doi.org/10.30931/jetas.1338660","url":null,"abstract":"In this paper, we first define the vector product in a special analog Minkowski Geometry $(mathbb{R}^3,langle,rangle) $ which is identified with the space of spatial hybrids. Next, we derive the Frenet-Serret frame formulae for a three dimensional non-parabolic curve by using the spatial hybrids and the vector product. However, we present the Frenet-Serret Frame formulae of a non-lightlike hybrid curve in $mathbb{R}^4$ and an illustrative example for all theorems of the paper with Matlab codes.","PeriodicalId":7757,"journal":{"name":"Anadolu University Journal of Science and Technology-A Applied Sciences and Engineering","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135831090","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, a nonlinear robust adaptive trajectory tracking control architecture based on Incremental Nonlinear Dynamic Inversion (INDI) is introduced to stabilize and control a quadrotor in presence of actuator partial fault. In a novel approach, a three-loop cascade architecture of the controller is proposed. The INDI algorithm is applied as the baseline controller in the inner-loop and a nonlinear model reference adaptive controller is augmented in the outer-loop to provide robustness for the unmodeled fault in the inner-loop. In the proposed control strategy, a modified PID controller is introduced in the most outer-loop for tracking the desired path. The fault effect has been modeled by considering the sudden variations of motor thrust and torques. To increase the robustness of the control algorithm the projection operator has been applied in the robust adaptive structure. The performance of the proposed controller is compared with a previous successful algorithm, which had been implemented on a quadrotor model. The results demonstrate that the proposed controller can provide full controllability of the desired faulty quadrotor in pitch, roll, and yaw channels in presence of partial fault of actuator up to 50%.
{"title":"Robust Adaptive Control Based on Incremental Nonlinear Dynamic Inversion for a Quadrotor in Presence of Partial Actuator Fault","authors":"Karim AHMADİ DASTGERDİ, D. Asadi, Seyed Yaser NABAVİ CHASHMİ, Önder Tutsoy","doi":"10.30931/jetas.1169518","DOIUrl":"https://doi.org/10.30931/jetas.1169518","url":null,"abstract":"In this paper, a nonlinear robust adaptive trajectory tracking control architecture based on Incremental Nonlinear Dynamic Inversion (INDI) is introduced to stabilize and control a quadrotor in presence of actuator partial fault. In a novel approach, a three-loop cascade architecture of the controller is proposed. The INDI algorithm is applied as the baseline controller in the inner-loop and a nonlinear model reference adaptive controller is augmented in the outer-loop to provide robustness for the unmodeled fault in the inner-loop. In the proposed control strategy, a modified PID controller is introduced in the most outer-loop for tracking the desired path. The fault effect has been modeled by considering the sudden variations of motor thrust and torques. To increase the robustness of the control algorithm the projection operator has been applied in the robust adaptive structure. The performance of the proposed controller is compared with a previous successful algorithm, which had been implemented on a quadrotor model. The results demonstrate that the proposed controller can provide full controllability of the desired faulty quadrotor in pitch, roll, and yaw channels in presence of partial fault of actuator up to 50%.","PeriodicalId":7757,"journal":{"name":"Anadolu University Journal of Science and Technology-A Applied Sciences and Engineering","volume":"107 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85510252","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 study presented the evaluation of the adsorption of Eriochrome Black T (EBT) on the activated carbon (trH-BS) produced from pepper stalk by activating with 50% phosphoric acid solution (H3PO4) and then by carbonizing at 650 oC for 30 min. in atmosphere of nitrogen (N2) was presented. The isotherm of trH-BS was Type IV, representing micro, meso and macroporous structures. The micropore volume and micropore surface area values of trH-BS were 0.39 cc/g and 1107.294 m2/g, respectively. Also, its meso and macropores had a volume of about 15-17 cc/g and an average surface area of 400 m2/g. The adsorption energy was 18.156 kJ/mol and the BET surface area was 756.257 m2/g. The structure of trH-BS was clarified structurally and morphologically and the formations like nano rod were seen at Scanning Electron Microscopy (SEM) images. By using trH-BS, the adsorption of EBT from the aqueous medium was investigated using 5 different parameters. As a result, it was found that the adsorbents obtained from pepper stalks are suitable for use in EBT adsorption with a ratio of about 50% under suitable conditions.
采用50%磷酸(H3PO4)活化后，在氮气(N2)气氛下于650℃下炭化30 min，考察了Eriochrome Black T (EBT)对辣椒秸秆活性炭的吸附性能。trH-BS等温线为IV型，分别代表微孔、介孔和大孔结构。trH-BS的微孔体积和微孔表面积分别为0.39 cc/g和1107.294 m2/g。中孔和大孔的体积约为15 ~ 17 cc/g，平均表面积为400 m2/g。吸附能为18.156 kJ/mol, BET表面积为756.257 m2/g。通过扫描电镜(SEM)对trH-BS的结构和形态进行了澄清，并观察到纳米棒状结构。采用trH-BS，研究了5种不同参数对EBT的吸附效果。实验结果表明，在适宜的条件下，辣椒秸秆吸附剂的吸附比约为50%，可用于EBT吸附。
{"title":"THE ADSORPTION PERFORMANCE and CHARACTERIZATION of THE ACTIVATED CARBON PRODUCED FROM PEPPER STALKS","authors":"H. Dolaş","doi":"10.30931/jetas.1145856","DOIUrl":"https://doi.org/10.30931/jetas.1145856","url":null,"abstract":"This study presented the evaluation of the adsorption of Eriochrome Black T (EBT) on the activated carbon (trH-BS) produced from pepper stalk by activating with 50% phosphoric acid solution (H3PO4) and then by carbonizing at 650 oC for 30 min. in atmosphere of nitrogen (N2) was presented. The isotherm of trH-BS was Type IV, representing micro, meso and macroporous structures. The micropore volume and micropore surface area values of trH-BS were 0.39 cc/g and 1107.294 m2/g, respectively. Also, its meso and macropores had a volume of about 15-17 cc/g and an average surface area of 400 m2/g. The adsorption energy was 18.156 kJ/mol and the BET surface area was 756.257 m2/g. The structure of trH-BS was clarified structurally and morphologically and the formations like nano rod were seen at Scanning Electron Microscopy (SEM) images. By using trH-BS, the adsorption of EBT from the aqueous medium was investigated using 5 different parameters. As a result, it was found that the adsorbents obtained from pepper stalks are suitable for use in EBT adsorption with a ratio of about 50% under suitable conditions.","PeriodicalId":7757,"journal":{"name":"Anadolu University Journal of Science and Technology-A Applied Sciences and Engineering","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87180491","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}
Social media has become an integral part of our world including private and work life. However, the rapid expansion and popularity of social media have resulted in the emergence of fake accounts. Fake accounts users often engage in misbehavior such as malicious activities, spread misinformation etc. The aim of this study is to perform an effective fake account detection by using ensemble learning methods (Bagging, Boosting, Stacking, Voting and Blending) in detecting fake social media accounts. The techniques are combined with various machine learning algorithms to measure their effectiveness in detecting fake accounts. The experimental results suggest that Bagging technique attains an accuracy level of 90.441%, Stacking technique attains 89.706%, Voting technique attains 88.971% and the Blending technique attains 88.235% in the test phase. While for the Boosting methods, XGboost technique attains accuracy level of 86.765%, whereas the AdaBoost outperforms it with an accuracy level of 91.912% in the test phase. The extant results denote that ensemble methods and their algorithms are effective and efficient in detecting fake social media accounts. Additional studies with larger datasets alongside the usage of different ensemble methods can further improve the accuracy of the detection process.
{"title":"A COMPARATIVE ANALYSIS OF ENSEMBLE LEARNING METHODS ON SOCIAL MEDIA ACCOUNT DETECTION","authors":"Tuğba TUNÇ ABUBAKAR, Merve Varol Arısoy","doi":"10.30931/jetas.1325483","DOIUrl":"https://doi.org/10.30931/jetas.1325483","url":null,"abstract":"Social media has become an integral part of our world including private and work life. However, the rapid expansion and popularity of social media have resulted in the emergence of fake accounts. Fake accounts users often engage in misbehavior such as malicious activities, spread misinformation etc. The aim of this study is to perform an effective fake account detection by using ensemble learning methods (Bagging, Boosting, Stacking, Voting and Blending) in detecting fake social media accounts. The techniques are combined with various machine learning algorithms to measure their effectiveness in detecting fake accounts. The experimental results suggest that Bagging technique attains an accuracy level of 90.441%, Stacking technique attains 89.706%, Voting technique attains 88.971% and the Blending technique attains 88.235% in the test phase. While for the Boosting methods, XGboost technique attains accuracy level of 86.765%, whereas the AdaBoost outperforms it with an accuracy level of 91.912% in the test phase. The extant results denote that ensemble methods and their algorithms are effective and efficient in detecting fake social media accounts. Additional studies with larger datasets alongside the usage of different ensemble methods can further improve the accuracy of the detection process.","PeriodicalId":7757,"journal":{"name":"Anadolu University Journal of Science and Technology-A Applied Sciences and Engineering","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76823317","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 research proposes a new efficient algorithm for calculating the square root function of the large-scale nonsingular sparse matrix by restarting the Heavy Ball Algorithm. The square root matrix function is critical in various applications, including signal processing, image processing, and machine learning. However, its computation is challenging due to existing methods' high computational complexity and numerical instability. The restarted Heavy Ball Algorithm provides a streamlined and efficient approach for computing the square root matrix function. The approach demonstrates its effectiveness through numerical experiments on various matrices, showing its superior performance compared to existing state-of-the-art methods. Numerical results show that the restarted Heavy Ball algorithm is feasible and effective for calculating the square root function.
{"title":"Streamlining Square Root Matrix Function Computation with Restarted Heavy Ball Algorithm","authors":"G. Karaduman","doi":"10.30931/jetas.1298099","DOIUrl":"https://doi.org/10.30931/jetas.1298099","url":null,"abstract":"This research proposes a new efficient algorithm for calculating the square root function of the large-scale nonsingular sparse matrix by restarting the Heavy Ball Algorithm. The square root matrix function is critical in various applications, including signal processing, image processing, and machine learning. However, its computation is challenging due to existing methods' high computational complexity and numerical instability. The restarted Heavy Ball Algorithm provides a streamlined and efficient approach for computing the square root matrix function. The approach demonstrates its effectiveness through numerical experiments on various matrices, showing its superior performance compared to existing state-of-the-art methods. Numerical results show that the restarted Heavy Ball algorithm is feasible and effective for calculating the square root function.","PeriodicalId":7757,"journal":{"name":"Anadolu University Journal of Science and Technology-A Applied Sciences and Engineering","volume":"151 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75841015","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. Rentsen, Bayartugs Tamjav, Ulziibayar Vandandoo
In this paper, we consider a multiplicative optimal control problem subject to a system of linear differential equation.It has been shown that product of two concave functions defined positively over a feasible set is quasiconcave. It allows us to consider the original problem from a view point of quasiconvex maximization theory and algorithm. Global optimality conditions use level set of the objective function and convex programming as subproblem. The objective function is product of two concave functions. We consider minimization of the objective functional. The problem is nonconvex optimal control and application of Pontriyagin’s principle does not always guarantee finding a global optimal control. Based on global optimality conditions, we develop an algorithm for solving the minimization problem globally.
{"title":"Multiplicative Optimal Control Problem","authors":"E. Rentsen, Bayartugs Tamjav, Ulziibayar Vandandoo","doi":"10.5564/jasea.v4i1.2684","DOIUrl":"https://doi.org/10.5564/jasea.v4i1.2684","url":null,"abstract":"In this paper, we consider a multiplicative optimal control problem subject to a system of linear differential equation.It has been shown that product of two concave functions defined positively over a feasible set is quasiconcave. It allows us to consider the original problem from a view point of quasiconvex maximization theory and algorithm. Global optimality conditions use level set of the objective function and convex programming as subproblem. The objective function is product of two concave functions. We consider minimization of the objective functional. The problem is nonconvex optimal control and application of Pontriyagin’s principle does not always guarantee finding a global optimal control. Based on global optimality conditions, we develop an algorithm for solving the minimization problem globally.","PeriodicalId":7757,"journal":{"name":"Anadolu University Journal of Science and Technology-A Applied Sciences and Engineering","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80794322","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, we obtain one-Lee weight codes over a class of nonchain rings and study their structures. We give an explicit construction for one-Lee weight codes. A method to derive more one-Lee weight codes from given a one-Lee weight code is also represented. By defining and making use of a distance-preserving Gray map, we get a family of optimal one-Hamming weight codes over finite fields.
{"title":"One weight codes over the ring F_q[v]/(v^s-v)","authors":"","doi":"10.30931/jetas.1152408","DOIUrl":"https://doi.org/10.30931/jetas.1152408","url":null,"abstract":"In this study, we obtain one-Lee weight codes over a class of nonchain rings and study their structures. \u0000We give an explicit construction for one-Lee weight codes. A method to derive more one-Lee weight codes from given a one-Lee weight code is also represented. By defining and making use of a distance-preserving Gray map, we get a family of optimal one-Hamming weight codes over finite fields.","PeriodicalId":7757,"journal":{"name":"Anadolu University Journal of Science and Technology-A Applied Sciences and Engineering","volume":"72 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88117515","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 study aimed to determine the effective doses of the cardiologist, nurses, and technical staff in the pediatric angiography laboratory during their diagnostic and therapeutic applications. This study is also to compare the radiation dose in the applications performed in the country with the effective doses exposed on a world scale. A total of 39 coronary angiography(CA)+percutaneous transluminal angioplasty(PTCA) methods were performed in the pediatric angiography laboratory during the study. The radiation dose received for each person in a single application was determined, and the total dose values were measured in the sequential applications. If the annual workload is taken into consideration, it is calculated that the person with a high workload may be exposed to a dose of 1384.7 μSv per year. Furthermore, from the total effective dose values, the doses per procedure were calculated to be in the range of 6.5 to 11.1 μSv. These results are consistent with the literature.
{"title":"OCCUPATIONAL RADIATION DOSE OF PERSONAL IN PEDIATRIC INTERVENTIONAL CARDIOLOGY","authors":"Kevser HIŞIROĞLU AYAR, E. Kam, D. Yaşar","doi":"10.30931/jetas.1147340","DOIUrl":"https://doi.org/10.30931/jetas.1147340","url":null,"abstract":"This study aimed to determine the effective doses of the cardiologist, nurses, and technical staff in the pediatric angiography laboratory during their diagnostic and therapeutic applications. This study is also to compare the radiation dose in the applications performed in the country with the effective doses exposed on a world scale. A total of 39 coronary angiography(CA)+percutaneous transluminal angioplasty(PTCA) methods were performed in the pediatric angiography laboratory during the study. The radiation dose received for each person in a single application was determined, and the total dose values were measured in the sequential applications. If the annual workload is taken into consideration, it is calculated that the person with a high workload may be exposed to a dose of 1384.7 μSv per year. Furthermore, from the total effective dose values, the doses per procedure were calculated to be in the range of 6.5 to 11.1 μSv. These results are consistent with the literature.","PeriodicalId":7757,"journal":{"name":"Anadolu University Journal of Science and Technology-A Applied Sciences and Engineering","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78484831","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}
Hidrostatik yataklar, yüksek basınçlı ve nispeten ince yağ filmleri sayesinde, yüksek sönümleme, rijitlik ve yük kapasitesi gibi avantajlarının yanında son derece düşük hareket hataları potansiyeline sahiptir. Genellikle boyutsal ve geometrik toleranslar son derece yüksek hassas olduğundan birçok makine üreticisi de kendi hidrostatik yatak sistemlerini tasarlamayı ve üretmeyi tercih etmektedirler. Bu makalenin amacı, bir eksenel hidrostatik yatağın performansını değerlendirebilecek ve yatak tasarımına yardımcı olabilecek bir analitik modeli gerçekleştirmektir. Böylece hidrostatik yatak geometrilerinin yük kapasitesi, gerekli debi, rijitlik, ve güç tüketimi için hesaplamaları yapılabilecektir. Aynı zamanda performans üzerinde etkili olan tasarım parametrelerinin cevap yüzeyi yöntemi (CYM) kullanılarak bir değerlendirilmesi de yapılarak optimal tasarımlar elde edilecektir.
{"title":"Eksenel Hidrostatik Yatak Tasarımı için Analitik Model ve Tasarım Parametrelerinin CYM ile Değerlendirilmesi","authors":"Zekeriya Parlak, Seçkin Çelebi̇, Gürkan Topbaş","doi":"10.30931/jetas.1116435","DOIUrl":"https://doi.org/10.30931/jetas.1116435","url":null,"abstract":"Hidrostatik yataklar, yüksek basınçlı ve nispeten ince yağ filmleri sayesinde, yüksek sönümleme, rijitlik ve yük kapasitesi gibi avantajlarının yanında son derece düşük hareket hataları potansiyeline sahiptir. Genellikle boyutsal ve geometrik toleranslar son derece yüksek hassas olduğundan birçok makine üreticisi de kendi hidrostatik yatak sistemlerini tasarlamayı ve üretmeyi tercih etmektedirler. Bu makalenin amacı, bir eksenel hidrostatik yatağın performansını değerlendirebilecek ve yatak tasarımına yardımcı olabilecek bir analitik modeli gerçekleştirmektir. Böylece hidrostatik yatak geometrilerinin yük kapasitesi, gerekli debi, rijitlik, ve güç tüketimi için hesaplamaları yapılabilecektir. Aynı zamanda performans üzerinde etkili olan tasarım parametrelerinin cevap yüzeyi yöntemi (CYM) kullanılarak bir değerlendirilmesi de yapılarak optimal tasarımlar elde edilecektir.","PeriodicalId":7757,"journal":{"name":"Anadolu University Journal of Science and Technology-A Applied Sciences and Engineering","volume":"80 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87376992","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}
Hybrid numbers which are accepted as a generalization of complex, hyperbolic and dual numbers, have attracted the attention of many researchers recently. In this paper, hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers are defined. Then some algebraic and combinatoric properties of these hybrinomials are examined such as the recurrence relations, summation formulas and generation functions. Additionally, hybrid hyper-Fibonacci and hybrid hyper-Lucas numbers are defined by using the hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers.
{"title":"Hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers","authors":"Efruz Özlem Mersin","doi":"10.30931/jetas.1196595","DOIUrl":"https://doi.org/10.30931/jetas.1196595","url":null,"abstract":"Hybrid numbers which are accepted as a generalization of complex, hyperbolic and dual numbers, have attracted the attention of many researchers recently. In this paper, hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers are defined. Then some algebraic and combinatoric properties of these hybrinomials are examined such as the recurrence relations, summation formulas and generation functions. Additionally, hybrid hyper-Fibonacci and hybrid hyper-Lucas numbers are defined by using the hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers.","PeriodicalId":7757,"journal":{"name":"Anadolu University Journal of Science and Technology-A Applied Sciences and Engineering","volume":"238 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77602035","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：