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学者姓名：钟展良
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A Lucas polynomial sequence is a pair of generalized polynomial sequences that satisfy the Lucas recurrence relation. Special cases include Fibonacci polynomials, Lucas polynomials, and Balancing polynomials. We define the ( a, b ) -type Lucas polynomial sequences and prove that their Melham's sums have some interesting divisibility properties. Results in this paper generalize the original Melham's conjectures.
Keyword ：
Fibonacci sequence Fibonacci sequence Lucas polynomial sequence Lucas polynomial sequence Lucas sequence Lucas sequence Melham's conjectures Melham's conjectures
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| GB/T 7714 | Chung, Chan-Liang , Zhong, Chunmei . Melham's sums for some Lucas polynomial sequences [J]. | NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS , 2024 , 30 (2) : 383-409 . |
| MLA | Chung, Chan-Liang 等. "Melham's sums for some Lucas polynomial sequences" . | NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS 30 . 2 (2024) : 383-409 . |
| APA | Chung, Chan-Liang , Zhong, Chunmei . Melham's sums for some Lucas polynomial sequences . | NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS , 2024 , 30 (2) , 383-409 . |
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云计算与物联网安全课程是信息安全专业本科生的必修课,培养学生运用所学的云计算与物联网技术分析和解决问题.本教学创新成果报告围绕3个课堂教学真实问题:一是学生多学科交叉基础知识不足;二是学生解决实际问题和实践能力不足;三是存在产学落差,学生所学技术无法符合产业需求.并且分别提出3个教学方案解决对应的课堂教学真实问题:一是开发"AI助教"APP,以增强现实(AR)和人工智能(AI)语音问答协助学生的学习过程,结合创新性;二是引入心率带、脑波仪、机器人等设备,强化学生的自主学习动机和学习习惯,培养学生解决问题的思维能力,提升高阶性;三是结合"码云"分享开源代码,由企业下载和评价,增加挑战度.
Keyword ：
人工智能 人工智能 信息教育 信息教育 物联网 物联网
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| GB/T 7714 | 吴伶 , 李小燕 , 陈志华 et al. 人工智能与增强现实应用于本科教育 [J]. | 科学咨询 , 2024 , (4) : 131-134 . |
| MLA | 吴伶 et al. "人工智能与增强现实应用于本科教育" . | 科学咨询 4 (2024) : 131-134 . |
| APA | 吴伶 , 李小燕 , 陈志华 , 钟展良 . 人工智能与增强现实应用于本科教育 . | 科学咨询 , 2024 , (4) , 131-134 . |
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We define the incomplete generalized bivariate Fibonacci p-polynomials and the incomplete generalized bivariate Lucas p-polynomials. We study their recursive relations and derive an interesting relationship through their generating functions. Subsequently, we prove an incomplete version of the well-known Fibonacci-Lucas relation and make some extensions to the relation involving incomplete generalized bivariate Fibonacci and Lucas p-polynomials. An argument about going from the regular to the incomplete Fibonacci-Lucas relation is discussed. We provide a relation involving the incomplete Leonardo and the incomplete Lucas-Leonardo p-numbers as an illustration.
Keyword ：
bivariate Fibonacci p-polynomials bivariate Fibonacci p-polynomials Fibonacci-Lucas relation Fibonacci-Lucas relation incomplete generalized bivariate Fibonacci p-polynomials incomplete generalized bivariate Fibonacci p-polynomials
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| GB/T 7714 | Zhong, Jingyang , Yao, Jialing , Chung, Chan-Liang . A Note on Incomplete Fibonacci-Lucas Relations [J]. | SYMMETRY-BASEL , 2023 , 15 (12) . |
| MLA | Zhong, Jingyang et al. "A Note on Incomplete Fibonacci-Lucas Relations" . | SYMMETRY-BASEL 15 . 12 (2023) . |
| APA | Zhong, Jingyang , Yao, Jialing , Chung, Chan-Liang . A Note on Incomplete Fibonacci-Lucas Relations . | SYMMETRY-BASEL , 2023 , 15 (12) . |
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Based on the method of generating functions of the sequence of Fibonacci k-step and Lucas k-step polynomials, or on a crucial identity relating Fibonacci k-step and Lucas k-step polynomials, extensions of Sury’s relation and the alternating Sury’s relation involving Fibonacci k-step and Lucas k-step polynomials are derived, respectively. Extensions of Sury’s relation involving Fibonacci-type and Lucas-type polynomials are also obtained. Of course, these relations are generalizations of the well-known Fibonacci-Lucas relation. © 2023, Colgate University. All rights reserved.
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| GB/T 7714 | Chung, C.-L. , Yao, J. , Zhou, K. . EXTENSIONS OF SURY’S RELATION INVOLVING FIBONACCI k-STEP AND LUCAS k-STEP POLYNOMIALS [J]. | Integers , 2023 , 23 . |
| MLA | Chung, C.-L. et al. "EXTENSIONS OF SURY’S RELATION INVOLVING FIBONACCI k-STEP AND LUCAS k-STEP POLYNOMIALS" . | Integers 23 (2023) . |
| APA | Chung, C.-L. , Yao, J. , Zhou, K. . EXTENSIONS OF SURY’S RELATION INVOLVING FIBONACCI k-STEP AND LUCAS k-STEP POLYNOMIALS . | Integers , 2023 , 23 . |
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This study proposes a multiple linear regression architecture based on stream homomorphic encryption computing to analyze ciphertext for massive secure data computing. The proposed architecture contains three subsystems including terminal subsystem, data access subsystem, and data computing subsystem. The method used behind the presented architecture contains four stages which are data preprocessing stage, data access stage, data computing stage, and result processing stage. In the practical experiments, a case study of traffic information prediction was selected to evaluate the proposed system and method. The predicted traffic information was generated by the proposed method in accordance with the encrypted traffic information. Our experimental results showed that the proposed architecture can effectively and promptly obtain the predicted traffic information.
Keyword ：
homomorphic encryption homomorphic encryption multiple linear regression multiple linear regression real-time streaming data analysis real-time streaming data analysis
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| GB/T 7714 | Zhang, Yi-Zhuo , Liu, Yiwei , Chung, Chan-Liang et al. Multiple Linear Regression Based on Stream Homomorphic Encryption Computing [C] . 2021 : 533-536 . |
| MLA | Zhang, Yi-Zhuo et al. "Multiple Linear Regression Based on Stream Homomorphic Encryption Computing" . (2021) : 533-536 . |
| APA | Zhang, Yi-Zhuo , Liu, Yiwei , Chung, Chan-Liang , Chen, Chi-Hua , Hwang, Feng-Jang . Multiple Linear Regression Based on Stream Homomorphic Encryption Computing . (2021) : 533-536 . |
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This article focuses on searching and classifying balancing numbers in a set of arithmetic progressions. The sufficient and necessary conditions for the existence of balancing numbers are presented. Moreover, explicit formulae of balancing numbers and various relations are included.
Keyword ：
(a (a balancing numbers balancing numbers b)-type balancing numbers b)-type balancing numbers Pell equation Pell equation sequence balancing numbers sequence balancing numbers
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| GB/T 7714 | Chung, Chan-Liang , Zhong, Chunmei , Zhou, Kanglun . Balances in the Set of Arithmetic Progressions [J]. | AXIOMS , 2021 , 10 (4) . |
| MLA | Chung, Chan-Liang et al. "Balances in the Set of Arithmetic Progressions" . | AXIOMS 10 . 4 (2021) . |
| APA | Chung, Chan-Liang , Zhong, Chunmei , Zhou, Kanglun . Balances in the Set of Arithmetic Progressions . | AXIOMS , 2021 , 10 (4) . |
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In this paper we shall define the special-valued multiple Hurwitz zeta functions, namely the multiple t-values t(alpha) and define similarly the multiple star t-values as t(alpha). Then we consider the sum of all such multiple (star) t-values of fixed depth and weight with even argument and prove that such a sum can be evaluated when the evaluations of t({2m}(n)) and t*({2m}(n)) are clear. We give the evaluations of them in terms of the classical Euler numbers through their generating functions.
Keyword ：
generating functions generating functions Hurwitz zeta function Hurwitz zeta function infinite series and products infinite series and products multiple zeta value multiple zeta value sum formula sum formula
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| GB/T 7714 | Chung, Chan-Liang . On the sum relation of multiple Hurwitz zeta functions [J]. | QUAESTIONES MATHEMATICAE , 2019 , 42 (3) : 297-305 . |
| MLA | Chung, Chan-Liang . "On the sum relation of multiple Hurwitz zeta functions" . | QUAESTIONES MATHEMATICAE 42 . 3 (2019) : 297-305 . |
| APA | Chung, Chan-Liang . On the sum relation of multiple Hurwitz zeta functions . | QUAESTIONES MATHEMATICAE , 2019 , 42 (3) , 297-305 . |
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Abstract ：
We give some polynomial sequence relations that are generalizations of the Sury-type identities. We provide two proofs, one based on an elementary identity and the other using the method of generating functions.
Keyword ：
Fibonacci sequence Fibonacci sequence generating function generating function Lucas sequence Lucas sequence polynomial sequence polynomial sequence
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| GB/T 7714 | Chung, Chan-Liang . Some Polynomial Sequence Relations [J]. | MATHEMATICS , 2019 , 7 (8) . |
| MLA | Chung, Chan-Liang . "Some Polynomial Sequence Relations" . | MATHEMATICS 7 . 8 (2019) . |
| APA | Chung, Chan-Liang . Some Polynomial Sequence Relations . | MATHEMATICS , 2019 , 7 (8) . |
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