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Analysis of the periodic solutions of a smooth and discontinuous oscillator 被引量:2
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作者 Zhi-Xin Li Qing-Jie Cao +1 位作者 Marian Wiercigroch Alain Léger 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2013年第4期575-582,共8页
In this paper, the periodic solutions of the smooth and discontinuous (SD) oscillator, which is a strongly irra- tional nonlinear system are discussed for the system having a viscous damping and an external harmonic... In this paper, the periodic solutions of the smooth and discontinuous (SD) oscillator, which is a strongly irra- tional nonlinear system are discussed for the system having a viscous damping and an external harmonic excitation. A four dimensional averaging method is employed by using the complete Jacobian elliptic integrals directly to obtain the perturbed primary responses which bifurcate from both the hyperbolic saddle and the non-hyperbolic centres of the un- perturbed system. The stability of these periodic solutions is analysed by examining the four dimensional averaged equa- tion using Lyapunov method. The results presented herein this paper are valid for both smooth (e 〉 0) and discontin- uous (ce = 0) stages providing the answer to the question why the averaging theorem spectacularly fails for the case of medium strength of external forcing in the Duffing system analysed by Holmes. Numerical calculations show a good agreement with the theoretical predictions and an excellent efficiency of the analysis for this particular system, which also suggests the analysis is applicable to strongly nonlinear systems. 展开更多
关键词 SD oscillator ~ Averaging method. Periodic so-lution ~ Irrational nonlinearity ~ Elliptic integral
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FRACTIONAL INTEGRALS OF PERIODIC FUNCTIONS OF SEVERAL VARIABLES
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作者 Wang Shiming 《Analysis in Theory and Applications》 1993年第1期82-96,共15页
In this paper it has been systematically studied the imbedding properties o f fractional integral operators of periodic functions of several variables,and isomorphic properties of fractional intregral operators in the... In this paper it has been systematically studied the imbedding properties o f fractional integral operators of periodic functions of several variables,and isomorphic properties of fractional intregral operators in the spaces of Lipschitz continuous functions. It has also been proved that the space of fractional integration,the space of Lipschitz continuous functions and the Sobolev space are identical in L^2-norm.Results obtainedhere are not true for fractional integrals(or Riesz potentials)in R^n. 展开更多
关键词 TH FRACTIONAL INTEGRALS OF PERIODIC FUNCTIONS OF SEVERAL VARIABLES
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Fourier coefficients of restrictions of eigenfunctions
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作者 Emmett L.Wyman Yakun Xi Steve Zelditch 《Science China Mathematics》 SCIE CSCD 2023年第8期1849-1878,共30页
Let{e_(j)}be an orthonormal basis of Laplace eigenfunctions of a compact Riemannian manifold(M,g).Let H■M be a submanifold and{ψ_(k)}be an orthonormal basis of Laplace eigenfunctions of H with the induced metric.We ... Let{e_(j)}be an orthonormal basis of Laplace eigenfunctions of a compact Riemannian manifold(M,g).Let H■M be a submanifold and{ψ_(k)}be an orthonormal basis of Laplace eigenfunctions of H with the induced metric.We obtain joint asymptotics for the Fourier coefficients<γHe_(j),ψ_(k)>L^(2)(H)=∫He_(j),ψ_(k)dV_(H)of restrictionsγHe_(j)of e_(j)to H.In particular,we obtain asymptotics for the sums of the norm-squares of the Fourier coefficients over the joint spectrum{(μ_(k),λ_(j))}^(∞)_(j,k-0)of the(square roots of the)Laplacian△_(M)on M and the Laplacian△_(H)on H in a family of suitably‘thick'regions in R^(2).Thick regions include(1)the truncated coneμ_(k)/λ_(j)∈[a,b]■(0,1)andλ_(j)≤λ,and(2)the slowly thickening strip|μ_(k)-cλ_(j)|≤w(λ)andλ_(j)≤λ,where w(λ)is monotonic and 1■w(λ)≤λ^(1/2).Key tools for obtaining the asymptotics include the composition calculus of Fourier integral operators and a new multidimensional Tauberian theorem. 展开更多
关键词 EIGENFUNCTIONS period integrals Kuznecov formula
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3D image reconstruction with controllable spatial filtering based on correlation of multiple periodic functions in computational integral imaging
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作者 Jae-Young Jang Myungjin Cho Eun-Soo Kim 《Chinese Optics Letters》 SCIE EI CAS CSCD 2015年第3期22-26,共5页
We propose a novel method of slice image reconstruction with controllable spatial filtering by using the correlation of periodic delta-function arrays (PDFAs) with elemental images in computational integral imaging.... We propose a novel method of slice image reconstruction with controllable spatial filtering by using the correlation of periodic delta-function arrays (PDFAs) with elemental images in computational integral imaging. The multiple PDFAs, whose spatial periods correspond to object's depths with the elemental image array (EIA), can generate a set of spatially filtered EIAs for multiple object depths compared with the conventional method for the depth of a single object. We analyze a controllable spatial filtering effect by the proposed method. To show the feasibility of the proposed method, we carry out preliminary experiments for multiple objects and present the results. 展开更多
关键词 image reconstruction with controllable spatial filtering based on correlation of multiple periodic functions in computational integral imaging EIA
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