For positive integers N1,N2,...,Nn, let L = Z^n ＋ A and A =- N1Z x -…… x NnZ ＋ F be two rational periodic sets, where A ∩ （1/N1）Z x ... x （1/Nn）Z and F ∩ Z^n are finite sets with （A- A）∩Z^n = {0} and （F...For positive integers N1,N2,...,Nn, let L = Z^n ＋ A and A =- N1Z x -…… x NnZ ＋ F be two rational periodic sets, where A ∩ （1/N1）Z x ... x （1/Nn）Z and F ∩ Z^n are finite sets with （A- A）∩Z^n = {0} and （F- F）N （N1Z x.. x NnZ） = {0}. In this note, we shall determine conditions under which the tiling set L has universal spectrum A. We first obtain a criterion of universal spectra. This criterion combined with the properties of compatible pair yields many necessary and sufficient conditions for A to be a universal spectrum for L. We then show that, under some mild additional conditions, the conjecture of Lagarias and Szab5 is true. The results here extend the corresponding results of Lagarias, Szabo and Wang.展开更多
In this paper,a blind multiband spectrum sensing(BMSS)method requiring no knowledge of noise power,primary signal and wireless channel is proposed based on the K-means clustering(KMC).In this approach,the KMC algorith...In this paper,a blind multiband spectrum sensing(BMSS)method requiring no knowledge of noise power,primary signal and wireless channel is proposed based on the K-means clustering(KMC).In this approach,the KMC algorithm is used to identify the occupied subband set(OSS)and the idle subband set(ISS),and then the location and number information of the occupied channels are obtained according to the elements in the OSS.Compared with the classical BMSS methods based on the information theoretic criteria(ITC),the new method shows more excellent performance especially in the low signal-to-noise ratio(SNR)and the small sampling number scenarios,and more robust detection performance in noise uncertainty or unequal noise variance applications.Meanwhile,the new method performs more stablely than the ITC-based methods when the occupied subband number increases or the primary signals suffer multi-path fading.Simulation result verifies the effectiveness of the proposed method.展开更多
An ellipsoidal Fourier-bound convex model (EFB model) is proposed in the present paper to express the uncertainty of seismic excitation, and several methods of selecting parameters of the model are explained. An analy...An ellipsoidal Fourier-bound convex model (EFB model) is proposed in the present paper to express the uncertainty of seismic excitation, and several methods of selecting parameters of the model are explained. An analytical expression is obtained for the worst response of the single-degree-of-freedom (SDOF) system with the EFB model. A numerical simulation shows that the traditional prediction of maximum response can yield the value substantially lover than that predicted by the EFB model. This means that the traditional designing method based on standard seismic inputs may lead to unsafe design decisions.展开更多
基金Supported by National Natural Science Foundation of China (Grant No. 11171201)the Fundamental Research Fund for the Central University (Grant No. GK201001002)
文摘For positive integers N1,N2,...,Nn, let L = Z^n ＋ A and A =- N1Z x -…… x NnZ ＋ F be two rational periodic sets, where A ∩ （1/N1）Z x ... x （1/Nn）Z and F ∩ Z^n are finite sets with （A- A）∩Z^n = {0} and （F- F）N （N1Z x.. x NnZ） = {0}. In this note, we shall determine conditions under which the tiling set L has universal spectrum A. We first obtain a criterion of universal spectra. This criterion combined with the properties of compatible pair yields many necessary and sufficient conditions for A to be a universal spectrum for L. We then show that, under some mild additional conditions, the conjecture of Lagarias and Szab5 is true. The results here extend the corresponding results of Lagarias, Szabo and Wang.
基金Projects(61362018,61861019)supported by the National Natural Science Foundation of ChinaProject(1402041B)supported by the Jiangsu Province Postdoctoral Scientific Research Project,China+1 种基金Project(16A174)supported by the Scientific Research Fund of Hunan Provincial Education Department,ChinaProject([2016]283)supported by the Research Study and Innovative Experiment Project of College Students,China
文摘In this paper,a blind multiband spectrum sensing(BMSS)method requiring no knowledge of noise power,primary signal and wireless channel is proposed based on the K-means clustering(KMC).In this approach,the KMC algorithm is used to identify the occupied subband set(OSS)and the idle subband set(ISS),and then the location and number information of the occupied channels are obtained according to the elements in the OSS.Compared with the classical BMSS methods based on the information theoretic criteria(ITC),the new method shows more excellent performance especially in the low signal-to-noise ratio(SNR)and the small sampling number scenarios,and more robust detection performance in noise uncertainty or unequal noise variance applications.Meanwhile,the new method performs more stablely than the ITC-based methods when the occupied subband number increases or the primary signals suffer multi-path fading.Simulation result verifies the effectiveness of the proposed method.
文摘An ellipsoidal Fourier-bound convex model (EFB model) is proposed in the present paper to express the uncertainty of seismic excitation, and several methods of selecting parameters of the model are explained. An analytical expression is obtained for the worst response of the single-degree-of-freedom (SDOF) system with the EFB model. A numerical simulation shows that the traditional prediction of maximum response can yield the value substantially lover than that predicted by the EFB model. This means that the traditional designing method based on standard seismic inputs may lead to unsafe design decisions.
