In this paper, we firstly generalize the relations among the basis vectors of LLL reduced basis to semi k-reduced basis. Then we analyze the complexities of the nearest plane algorithm and round-off algorithm on semi ...In this paper, we firstly generalize the relations among the basis vectors of LLL reduced basis to semi k-reduced basis. Then we analyze the complexities of the nearest plane algorithm and round-off algorithm on semi k-reduced basis, which, compared with L. Babai's results on LLL reduced basis, have better approximate ratios and contain almost the same time complexities.展开更多
By means of F[x]-lattice basis reduction algorithm, a new algorithm is presented for synthesizing minimum length linear feedback shift registers (or minimal polynomials) for the given mul-tiple sequences over a field ...By means of F[x]-lattice basis reduction algorithm, a new algorithm is presented for synthesizing minimum length linear feedback shift registers (or minimal polynomials) for the given mul-tiple sequences over a field F. Its computational complexity is O(N2) operations in F where N is the length of each sequence. A necessary and sufficient condition for the uniqueness of minimal polynomi-als is given. The set and exact number of all minimal polynomials are also described when F is a finite field.展开更多
A longstanding challenge in materials science has been the computational modeling of interfaces between materials with different lattice parameters.Traditional approaches using plane-wave basis sets require either int...A longstanding challenge in materials science has been the computational modeling of interfaces between materials with different lattice parameters.Traditional approaches using plane-wave basis sets require either introducing artificial strain through unified lattice parameters or constructing prohibitively large supercells to accommodate the mismatch.These limitations have often deterred researchers from investigating large,mismatched interfaces,creating a gap in the understanding of these important systems.This work introduces an innovative algorithm that adaptively tunes the plane-wave basis sets to match the periodic structure of each material across the interface.By eliminating the need for extensive supercells or compromised lattice parameters,this new method reduces computational costs while retaining reliable results.The ability to efficiently calculate the eigen-energies of such mismatched systems,a crucial step for full density functional theory(DFT)calculations,is demonstrated with two dimensional versions of InAs/Si and SiC/Si interface potentials.展开更多
文摘In this paper, we firstly generalize the relations among the basis vectors of LLL reduced basis to semi k-reduced basis. Then we analyze the complexities of the nearest plane algorithm and round-off algorithm on semi k-reduced basis, which, compared with L. Babai's results on LLL reduced basis, have better approximate ratios and contain almost the same time complexities.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 19931010, G1999035804).
文摘By means of F[x]-lattice basis reduction algorithm, a new algorithm is presented for synthesizing minimum length linear feedback shift registers (or minimal polynomials) for the given mul-tiple sequences over a field F. Its computational complexity is O(N2) operations in F where N is the length of each sequence. A necessary and sufficient condition for the uniqueness of minimal polynomi-als is given. The set and exact number of all minimal polynomials are also described when F is a finite field.
基金support of The Boeing Company,as part of the Boeing-Technion Sustainable Aviation Fuel Innovation CenterWe sincerely thank Boeing for their valuable support and collaboration.This project was also conducted within the framework of the Guy Sella Memorial Project at Technion,established by SolarEdge Technologies LTD.Partial funding from The Israeli Sustainable Aviation Fuel Knowledge Center–iSAF,supported by The Israeli Ministry of Innovation,Science,and Technology,is gratefully acknowledgedThis article is based upon work from COST IG18234(NanoCatML),supported by COST(European Cooperation in Science and Technology)http://www.cost.eu.
文摘A longstanding challenge in materials science has been the computational modeling of interfaces between materials with different lattice parameters.Traditional approaches using plane-wave basis sets require either introducing artificial strain through unified lattice parameters or constructing prohibitively large supercells to accommodate the mismatch.These limitations have often deterred researchers from investigating large,mismatched interfaces,creating a gap in the understanding of these important systems.This work introduces an innovative algorithm that adaptively tunes the plane-wave basis sets to match the periodic structure of each material across the interface.By eliminating the need for extensive supercells or compromised lattice parameters,this new method reduces computational costs while retaining reliable results.The ability to efficiently calculate the eigen-energies of such mismatched systems,a crucial step for full density functional theory(DFT)calculations,is demonstrated with two dimensional versions of InAs/Si and SiC/Si interface potentials.
