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Formalization Of Matrix Theory In Hol4, Zhiping Shi, Yan Zhang, Zhenke Liu, Xinan Kang, Yong Guan, Jie Zhang, Xiaoyu Song
Formalization Of Matrix Theory In Hol4, Zhiping Shi, Yan Zhang, Zhenke Liu, Xinan Kang, Yong Guan, Jie Zhang, Xiaoyu Song
Yong Guan
Matrix theory plays an important role in modeling linear systems in engineering and science. To model and analyze the intricate behavior of complex systems, it is imperative to formalize matrix theory in a metalogic setting. This paper presents the higherorder logic (HOL) formalization of the vector space and matrix theory in the HOL4 theorem proving system. Formalized theories include formal definitions of real vectors and matrices, algebraic properties, and determinants, which are verified in HOL4. Two case studies, modeling and verifying composite two-port networks and state transfer equations, are presented to demonstrate the applicability and effectiveness of our work.
Fibonacci Sequence And Orderliness As Observed In The Creations Of Allah, Mohd Rezuan Masran Mr.
Fibonacci Sequence And Orderliness As Observed In The Creations Of Allah, Mohd Rezuan Masran Mr.
Mr. Mohd Rezuan Masran
There are numerous verses in the Quran that encourage Muslims to observe the many creations of Allah. This article is an exploratory discuss ion on the observation of a sequence of numbers known as the Fibonacci sequence (also known as the Fibonacci numbers ) which can be observed in the creations of Allah. The history of Fibonacci sequence dated back to 1202 in the magnum opus of the Italian mathematician, Leonardo Pisano Fibonacci, entitled Liber Abaci ( Book of Calculation ). This article discusses verses in the Quran that encourage us to observe Allah’s creations. T here are many occurrences …