Fibonacci sequence,generated by summing the preceding two terms,is a classical sequence renowned for its elegant properties.In this paper,leveraging properties of generalized Fibonacci sequences and formulas for conse...Fibonacci sequence,generated by summing the preceding two terms,is a classical sequence renowned for its elegant properties.In this paper,leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of equidistant sub-sequences,we investigate the ratio of the sum of numbers along main-diagonal and sub-diagonal of odd-order grids containing generalized Fibonacci sequences.We show that this ratio is solely dependent on the order of the grid,providing a concise and splendid identity.展开更多
The Advanced Encryption Standard(AES)is the most widely used symmetric cipher today.AES has an important place in cryptology.Finite field,also known as Galois Fields,are cornerstones for understanding any cryptography...The Advanced Encryption Standard(AES)is the most widely used symmetric cipher today.AES has an important place in cryptology.Finite field,also known as Galois Fields,are cornerstones for understanding any cryptography.This encryption method on AES is a method that uses polynomials on Galois fields.In this paper,we generalize the AES-like cryptology on 2×2 matrices.We redefine the elements of k-order Fibonacci polynomials sequences using a certain irreducible polynomial in our cryptology algorithm.So,this cryptology algorithm is called AES-like cryptology on the k-order Fibonacci polynomial matrix.展开更多
This paper investigates optical transport in metamaterial waveguide arrays(MMWAs)exhibiting Bloch-like oscillations(BLOs).The MMWAs is fabricated by laterally combining metal and dielectric layers in a Fibonacci seque...This paper investigates optical transport in metamaterial waveguide arrays(MMWAs)exhibiting Bloch-like oscillations(BLOs).The MMWAs is fabricated by laterally combining metal and dielectric layers in a Fibonacci sequence.By mapping the field distribution of Gaussian wave packets in these arrays,we directly visualize the mechanical evolution in a classical wave environment.Three distinct oscillation modes are observed at different incident positions in the ninth-generation Fibonacci structure,without introducing thickness or refractive index gradient in any layer.Additionally,the propagation period of BLOs increases with a redshift of the incident wavelength for both ninth-and tenth-generation Fibonacci MMWAs.These findings provide a valuable method for manipulating BLOs and offer new insights into optical transport in metamaterials,with potential applications in optical device and wave control technologies.展开更多
Zone plates play an important role in X-ray and optics fileds.In this work,we proposed a generalized Fibonacci zone plates(GFiZP)is proposed,which enables the manipulation of focusing properties for X-ray and light.Co...Zone plates play an important role in X-ray and optics fileds.In this work,we proposed a generalized Fibonacci zone plates(GFiZP)is proposed,which enables the manipulation of focusing properties for X-ray and light.Compared to conventional Fibonacci zone plates(FiZPs)and Cantor-type fractal zone plates(FraZPs),this device offers additional degrees of freedom for engineering focusing performance.In comparison with FraZPs,GFiZPs are constructed with inflation rule instead of extraction rule,thus avoiding sparse structures at high recursion orders,the sparse structures would lead to issues in fabrication.Notably,numerical simulations demonstrate that,similar to FraZPs,GFiZPs retain two critical functionalities:multi-focal capability and self-similar intensity distribution.Furthermore,we conducted a detailed investigation into the axial irradiance profiles of GFiZPs with varying structural parameters.Given these favorable properties,this novel zone plate design holds great potential for expanded applications in areas such as optical manufacturing and optical manipulation of microparticles.展开更多
To improve the traffic scheduling capability in operator data center networks,an analysis prediction and online scheduling mechanism(APOS)is designed,considering both the network structure and the network traffic in t...To improve the traffic scheduling capability in operator data center networks,an analysis prediction and online scheduling mechanism(APOS)is designed,considering both the network structure and the network traffic in the operator data center.Fibonacci tree optimization algorithm(FTO)is embedded into the analysis prediction and the online scheduling stages,the FTO traffic scheduling strategy is proposed.By taking the global optimal and the multi-modal optimization advantage of FTO,the traffic scheduling optimal solution and many suboptimal solutions can be obtained.The experiment results show that the FTO traffic scheduling strategy can schedule traffic in data center networks reasonably,and improve the load balancing in the operator data center network effectively.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12471298)the Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.23JSQ031)the Shaanxi Province College Student Innovation and Entrepreneurship Training Program(Grant Nos.S202210699481 and S202310699324X).
文摘Fibonacci sequence,generated by summing the preceding two terms,is a classical sequence renowned for its elegant properties.In this paper,leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of equidistant sub-sequences,we investigate the ratio of the sum of numbers along main-diagonal and sub-diagonal of odd-order grids containing generalized Fibonacci sequences.We show that this ratio is solely dependent on the order of the grid,providing a concise and splendid identity.
基金This work is supported by the Scientific Research Project(BAP)2020FEBE009,Pamukkale University,Denizli,Turkey.
文摘The Advanced Encryption Standard(AES)is the most widely used symmetric cipher today.AES has an important place in cryptology.Finite field,also known as Galois Fields,are cornerstones for understanding any cryptography.This encryption method on AES is a method that uses polynomials on Galois fields.In this paper,we generalize the AES-like cryptology on 2×2 matrices.We redefine the elements of k-order Fibonacci polynomials sequences using a certain irreducible polynomial in our cryptology algorithm.So,this cryptology algorithm is called AES-like cryptology on the k-order Fibonacci polynomial matrix.
文摘This paper investigates optical transport in metamaterial waveguide arrays(MMWAs)exhibiting Bloch-like oscillations(BLOs).The MMWAs is fabricated by laterally combining metal and dielectric layers in a Fibonacci sequence.By mapping the field distribution of Gaussian wave packets in these arrays,we directly visualize the mechanical evolution in a classical wave environment.Three distinct oscillation modes are observed at different incident positions in the ninth-generation Fibonacci structure,without introducing thickness or refractive index gradient in any layer.Additionally,the propagation period of BLOs increases with a redshift of the incident wavelength for both ninth-and tenth-generation Fibonacci MMWAs.These findings provide a valuable method for manipulating BLOs and offer new insights into optical transport in metamaterials,with potential applications in optical device and wave control technologies.
文摘Zone plates play an important role in X-ray and optics fileds.In this work,we proposed a generalized Fibonacci zone plates(GFiZP)is proposed,which enables the manipulation of focusing properties for X-ray and light.Compared to conventional Fibonacci zone plates(FiZPs)and Cantor-type fractal zone plates(FraZPs),this device offers additional degrees of freedom for engineering focusing performance.In comparison with FraZPs,GFiZPs are constructed with inflation rule instead of extraction rule,thus avoiding sparse structures at high recursion orders,the sparse structures would lead to issues in fabrication.Notably,numerical simulations demonstrate that,similar to FraZPs,GFiZPs retain two critical functionalities:multi-focal capability and self-similar intensity distribution.Furthermore,we conducted a detailed investigation into the axial irradiance profiles of GFiZPs with varying structural parameters.Given these favorable properties,this novel zone plate design holds great potential for expanded applications in areas such as optical manufacturing and optical manipulation of microparticles.
基金supported by National Natural Science Foundation of China(No.62163036).
文摘To improve the traffic scheduling capability in operator data center networks,an analysis prediction and online scheduling mechanism(APOS)is designed,considering both the network structure and the network traffic in the operator data center.Fibonacci tree optimization algorithm(FTO)is embedded into the analysis prediction and the online scheduling stages,the FTO traffic scheduling strategy is proposed.By taking the global optimal and the multi-modal optimization advantage of FTO,the traffic scheduling optimal solution and many suboptimal solutions can be obtained.The experiment results show that the FTO traffic scheduling strategy can schedule traffic in data center networks reasonably,and improve the load balancing in the operator data center network effectively.
