A λ-Lemma for Partially Hyperbolic Tori and the Obstruction Property

Using a scheme given by Marco, we prove that partially hyperbolic tori along resonant surfaces of near-integrable Hamiltonian systems possess the obstruction property in Arnold's terminology. The proof is based on a specific lambda lemma for these tori.     

A Criterion for Finite Topological Determinacy of Map-Germs

Let f, g: (Rⁿ, 0) (R^p, 0) be two C map-germs. Then f and gare C⁰-equivalent if there exist homeomorphism-germs h and lof (Rⁿ, 0) and (R^p, 0) respectively such that g = l f h^–1.Let k be a positive integer. A germ f is k-C⁰-determined ifevery germ g with j^k g(0) = j^k f(0) is C⁰-equivalent to f. Moreover,we say that f is finitely topologically determined if f is k-C⁰-determinedfor some finite k. We prove a theorem giving a sufficient conditionfor a germ to be finitely topologically determined. We explainthis condition below. Let N and P be two C manifolds. Consider the jet bundle J^k(N,P) with fiber J^k(n, p). Let z in J^k(n, p) and let f be suchthat z = j^kf(0). Define Whether (f) < k depends only on z, not on f. We can thereforedefine the set Let W^k(N, P) be the subbundle of J^k(N, P) with fiber W^k(n, p).Mather has constructed a finite Whitney (b)-regular stratificationS^k(n, p) of J^k(n, p) – W^k(n, p) such that all strata aresemialgebraic and K-invariant, having the property that if S^k(N,P) denotes the corresponding stratification of J^k(N, P) –W^k(N, P) and f C(N, P) is a C map such that j^kf is multitransverseto S^k(N, P), j^kf(N) W^k(N, P) = and N is compact (or f is proper),then f is topologically stable. For a map-germ f: (Rⁿ, 0) (R^p, 0), we define a certain ojasiewiczinequality. The inequality implies that there exists a representativef: U R^p such that j^kf(U – 0) W^k (Rⁿ, R^p = and suchthat j^kf is multitransverse to S^k (Rⁿ, R^p) at any finite setof points S U – 0. Moreover, the inequality controlsthe rate j^kf becomes non-transverse as we approach 0. We showthat if f satisfies this inequality, then f is finitely topologicallydetermined. 1991 Mathematics Subject Classification: 58C27.     

Capacitance-voltage behaviour inp-type ɛ-GaSe single crystal ∥c at different temperatures

Summary  Capacitance-voltage measurements have been carried out onp-type ɛ-GaSe single crystal ∥c in the temperature range 300 to 360 K, with applied voltages of -1, 0 and +1 V. TheC-V measurements in this temperature range have shown a shift in capacitanceC and conductanceG to the higher values with an increase in temperature. The depletion layer widthW, the Debye length L_D and the doping densityN _α have been worked out and plots ofN _α vs. W have shown a decrease inW with an increase in temperature. The plots of L_D vs. N _α vary as 1/N_α^1/2, which gives N_αL_D ⋍ 3.3 × 10¹¹ charges/m² for doping density of 10¹⁶m⁻³. The values ofG at different temperatures have been used to obtain the activation energies, which are found to be ΔE ⋍ 0.11 eV for -1 and +1 V applied voltages, and ΔE ⋍ 0.06 eV for zero volt. The authors of this paper have agreed to not receive the proofs for correction.     

Remarks on regular (LF)-spaces

Developing ideas found in a recent paper of Gilsdorf to arbitrary topological vector spaces (tvs) one shows that a Hausdorff (LB) _tv -spaceE is regular provided every null-sequence inE has a series convergent subsequence inE. Received by the editors 1980Mathematics Subject Classification (1985 Revision) 46A12.     

Advanced topology on the multiscale sequence spaces

We pursue the study of the multiscale spaces S^ν introduced by Jaffard in the context of multifractal analysis. We give the necessary and sufficient condition for S^ν to be locally p-convex, and exhibit a sequence of p-norms that defines its natural topology. The strong topological dual of S^ν is identified to another sequence space depending on ν, endowed with an inductive limit topology. As a particular case, we describe the dual of a countable intersection of Besov spaces.     

Kondo-insulating state in CeNi1−xRhxSn as a function of carrier number

Our systematic study has shown that the gap in doped CeNiSn Kondo insulator is very sensitive to the degree of hybridization V between the f-electron and conduction electron states. In the system CeNi_1−xRh_xSn, the carrier concentration diminishes upon Rh substitution for Ni. The transition from Kondo-insulator region to a metallic region is discussed as a function of variable valence electron number induced by substitution of Rh for Ni and of the accompanying effect of the change hybridization energy V.     

Topological aspect of disclinations in two-dimensional crystals

By using topological current theory, this paper studies the inner topological structure of disclinations during the melting of two-dimensional systems. From two-dimensional elasticity theory, it finds that there are topological currents for topological defects in homogeneous equation. The evolution of disclinations is studied, and the branch conditions for generating, annihilating, crossing, splitting and merging of disclinations are given.     

Topological aspects in a two-component Bose condensed system in neutron star

By making use of Duan--Ge's decomposition theory of gauge potential and the topological current theory proposed by Prof. Duan Yi-Shi, we study a two-component superfluid Bose condensed system, which is supposed to be realized in the interior of neutron stars in the form of the coexistence of a neutron superfluid and a protonic superconductor. We propose that this system possesses vortex lines. The topological charges of the vortex lines are characterized by the Hopf indices and the Brower degrees of φ-mapping.     

高亏格膜泡形状的数值计算

通过对Willmore区域外,特别是中等及较小约化体积下的形状及其演化进行深入细致的研究,发现在这一区域的形状要远比原有的猜测丰富,亏格g=2的膜泡会展现出比已有结果更多迷人的形状并出现新的膜泡相变分支.同时,数值计算的结果更加期待实验验证,从而为曲率模型的正确性提供有力支持.