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
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
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
A special class of cubic polynomials possessing decay of geometry property is studied.This class of cubic bimodal maps has generalized Fibonacci combinatorics.For maps with bounded combinatorics,we show that they have...A special class of cubic polynomials possessing decay of geometry property is studied.This class of cubic bimodal maps has generalized Fibonacci combinatorics.For maps with bounded combinatorics,we show that they have an absolutely continuous invariant probability measure.展开更多
The equitable total coloring of a graph G is a total coloring such that the numbers of elements in any two colors differ by at most one.The smallest number of colors needed for an equitable total coloring is called th...The equitable total coloring of a graph G is a total coloring such that the numbers of elements in any two colors differ by at most one.The smallest number of colors needed for an equitable total coloring is called the equitable total chromatic number.This paper contributes to the equitable total coloring of Fibonacci graphs F_(∆,n).We determine the equitable total chromatic numbers of F_(∆,n) for∆=3,4,5 and propose a conjecture on that for∆>=6.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.
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.
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A special class of cubic polynomials possessing decay of geometry property is studied.This class of cubic bimodal maps has generalized Fibonacci combinatorics.For maps with bounded combinatorics,we show that they have an absolutely continuous invariant probability measure.
基金Supported by the National Natural Science Foundation of China(Grant No.62072292)the Natural Science Foundation of Shandong Province(Grant No.ZR2020KF010).
文摘The equitable total coloring of a graph G is a total coloring such that the numbers of elements in any two colors differ by at most one.The smallest number of colors needed for an equitable total coloring is called the equitable total chromatic number.This paper contributes to the equitable total coloring of Fibonacci graphs F_(∆,n).We determine the equitable total chromatic numbers of F_(∆,n) for∆=3,4,5 and propose a conjecture on that for∆>=6.
