Parametric Characteristic Analysis for Generalized Frequency Response Functions of Nonlinear Systems

In order to explicitly reveal the relationship between system frequency response functions and model parameters which define system nonlinearities, and consequently unveil a direct connection from model parameters to system frequency response characteristics, a parametric characteristic analysis approach is proposed for Volterra systems described by a nonlinear differential equation (NDE). The parametric characteristics of the generalized frequency response functions (GFRFs) for the NDE model are established, and some important properties are discussed, which can explicitly reveal what model parameters contribute and how these parameters affect the GFRFs. Based on the parametric characteristic analysis, it is demonstrated how the system frequency domain characteristics are related to the system time domain model parameters and how the output frequency response function can now be determined explicitly with a detailed polynomial structure. These new results provide a significant and novel insight into the analysis and design of nonlinear systems in the frequency domain. Several examples are included to illustrate the results.     

Tails of Bipartite Distance-regular Graphs

Let Γ denote a bipartite distance-regular graph with diameterD  ≥  4 and valency k ≥  3. Let θ 0  > θ 1  >  >  θD denote the eigenvalues of Γ and let E₀, E₁, , E_Ddenote the associated primitive idempotents. Fix s(1  ≤  s ≤  D −  1 ) and abbreviate E: =  E_s. We say E is a tail whenever the entrywise product E   E is a linear combination of E₀, E and at most one other primitive idempotent of Γ. Letq_ij^{σi + 1 h} (0  ≤ h , i, j ≤  D) denote the Krein parameters of Γ and letΔ denote the undirected graph with vertices 0, 1, , D where two vertices i, j are adjacent whenever i ≠  =  j andq_ij^σi + 1s  ≠  =  0. We show E is a tail if and only if one of (i)–(iii) holds: (i) Δ is a path; (ii) Δ has two connected components, each of which is a path; (iii) D =  6 and Δ has two connected components, one of which is a path on four vertices and the other of which is a clique on three vertices.     

Extendability of Large-Scale Lipschitz Maps

Let be metric spaces, a subset of , and a large-scale lipschitz map. It is shown that possesses a large-scale lipschitz extension (with possibly larger constants) if is a Gromov hyperbolic geodesic space or the cartesian product of finitely many such spaces. No extension exists, in general, if is an infinite-dimensional Hilbert space. A necessary and sufficient condition for the extendability of a lipschitz map is given in the case when is separable and is a proper, convex geodesic space.

     

Magnetopolaron states involving confined phonons in a semiconductor quantum well

Energy splitting ΔE _res in double magnetopolaron energy spectrum in rectangular quantum wells as functions of the well width d have been calculated. We have considered in the capacity of interaction leading to resonant coupling between electrons and phonons the interaction with confined phonons and (for comparison) with bulk LO phonons. We have obtained the conditions when the interaction with bulk phonons yields correct results. Calculations for AlAs/GaAs/AlAs and AlSb/InSb/AlSb structures have been performed. Alongside the parameter ΔE _res for a polaron, whose resonant magnetic field is determined by the condition Ω=ω _L1, where Ω is the cyclotron frequency and ω _L1 is the LO phonon frequency in the quantum well (A-polaron), we have calculated ΔE _res for D-(Ω=2ω _L1) and F-polarons (Ω=3ω _L1), which is a factor of $\sqrt 2 $ and $\sqrt 3 $ , respectively, smaller than ΔE _res for the A-polaron. Since the splitting ΔE _res for the A-polaron is very large (up to 0.2?ω _L1), it is more convenient to study in experiments D-and F-polarons since their resonant magnetic fields are lower. We have predicted existence of “weak” magnetopolarons, in which the splitting is proportional to a higher power of Frölich’s coupling constant α than α ^1/2.     

Te溶剂垂直区熔法生长Φ20MCT晶体组分控制研究

采用Ｔｅ作溶剂在特制的垂直区熔炉上开展了Φ２０ＭＣＴ晶体的生长研究；详细阐述了该方法ＭＣＴ晶体的生长过程和生长机理；总结了分析了晶体生长过程中影响组分的因素；提出了生长过程中组分控制存在的问题和改善组分控制的措施。