Multi-separation, centrifugality and centripetality imply chaos

Let be an interval. need not be compact or bounded. Let be a continuous map, and be a trajectory of with or . Then there is a point such that . A point is called a centripetal point of relative to if or , and is centrifugal if or . In this paper we prove that if there exist centripetal points of in , then has periodic points of some odd () period . In addition, we also prove that if ) is multi-separated by Fix(), or there exists a centrifugal point of in , then is turbulent and hence has periodic points of all periods.

     

Synthesis and characterization of diphenylaminodiphenyl stryl based alternating copolymers

Diphenylaminobiphenylated stryl based alternating copolymers with phenyl or fluorene, which were expected to have a terphenylene vinylene backbone containing an (N,N‐diphenylamino)biphenyl pendant and a phenyl/fluorene/phenylene vinylene backbone containing an (N,N‐diphenylamino)biphenyl pendant, were synthesized by a Suzuki coupling reaction. The obtained copolymers were confirmed with various types of spectroscopy. The alternating copolymers showed good hole‐injection properties because of their low oxidation potential and good solubility and high thermal stability with a high glass‐transition temperature. The alternating copolymers showed blue emissions because of the adjusted conjugation lengths; the maximum wavelength was 460 nm for poly{4,4′‐biphenylene‐α‐[4″‐(N,N′‐diphenylamino)diphenyl]vinylene‐alt‐5‐(2′‐ethylhexyloxy)‐2‐methoxybenzene} and 487 nm for poly{4,4′‐biphenylene‐α‐[4″‐(N,N′‐diphenylamino)diphenyl] vinylene‐alt‐9,9‐dihexylfluorene}. The maximum brightness of indium tin oxide/poly(3,4‐ethylene dioxythiophene)/polymer/LiF/Al devices with poly{4,4′‐biphenylene‐α‐[4″‐(N,N′‐diphenylamino)diphenyl]vinylene‐alt‐5‐(2′‐ethylhexyloxy)‐2‐methoxybenzene} or poly{4,4′‐biphenylene‐α‐[4″‐(N,N′‐diphenylamino)diphenyl]vinylene‐alt‐9,9‐dihexylfluorene} as the emitting layer was 250 or 1000 cd/m², respectively. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 341–347, 2007     

掺CdSxSe1-x玻璃波导分布反馈光学双稳器件

本文给出了掺CdS_xSe_1-x玻璃平面波导分布反馈(DFB)光学双稳器件的设计和制备方法,实现了低功耗、快速的本征光学双稳。     

Selective absorption

Summary Some organic acids, alcohol and amine which have an asymmetric carbon atom were used for an investigation of asymmetric absorption on wool. Racemic mixture of hydratropic acid, mandelic acid andα-phenethylamine have shown the selective absorption on wool from their aqueous and alcoholic aqueous solutions and S-form of their diastereoisomers preferentially absorbed on wool. According to the results we obtained so far, it is concluded that the preferential absorption strongly depends on the configuration of the substance of which wool is composed.     

Specific heat measurement of the layered nitride superconductor Li(x)ZrNCl

Specific heat has been investigated in a layered nitride superconductor, Li(0.12)ZrNCl, with T(c)=12.7 K. The obtained data have shown a marked dichotomy: The specific heat jump at T(c) (DeltaC/gamma(n)T(c)=1.8) and the superconducting gap ratio (2Delta/k(B)T(c)=4.6-5.2) have indicated an intermediate to a strong coupling of electrons, while the upper limit of the electron-phonon coupling constant lambda has directly been estimated to be 0.22, which belongs to a weak coupling regime. Furthermore, the rapid increase of gamma as a function of magnetic field suggests that the present material has an anisotropic s wave gap.     

Determination of the orbital moment and crystal-field splitting in LaTiO3

Utilizing a sum rule in a spin-resolved photoelectron spectroscopic experiment with circularly polarized light, we show that the orbital moment in LaTiO3 is strongly reduced from its ionic value, both below and above the Ne el temperature. Using Ti L2,3 x-ray absorption spectroscopy as a local probe, we found that the crystal-field splitting in the t2g subshell is about 0.12-0.30 eV. This large splitting does not facilitate the formation of an orbital liquid.     

Nature of the well screened state in hard X-ray Mn 2p core-level photoemission measurements of La1-xSrxMnO3 films

Using hard x-ray (HX; hnu=5.95 keV) synchrotron photoemission spectroscopy (PES), we study the intrinsic electronic structure of La(1-x)Sr(x)MnO(3) (LSMO) thin films. Comparison of Mn 2p core-levels with soft x-ray (SX; hnu approximately 1000 eV) PES shows a clear additional well-screened feature only in HX PES. Takeoff-angle dependent data indicate its bulk (> or =20 A) character. The doping and temperature dependence track the ferromagnetism and metallicity of the LSMO series. Cluster model calculations including charge transfer from doping-induced states show good agreement, confirming this picture of bulk properties reflected in Mn 2p core-levels using HX PES.     

An Arc as the Inverse Limit of a Single Bonding Map of Type N on [0,1]

Let I = [0, 1], c ₁, c ₂ ∈ (0, 1) with c ₁ < c ₂ and f : I⊸I be a continuous map satisfying: are both strictly increasing and is strictly decreasing. Let A = {x ∈ [0, c ₁]∣f(x) = x}, a=max A, a ₁ =max(A\{a}), and B = {x ∈ [c ₂, 1]∣f(x) = x}, b=minB, b ₁ =min(B\{b}). Then the inverse limit (I, f) is an arc if and only if one of the following three conditions holds: (1) If c ₁ < f (c ₁) ≤ c ₂ (resp. c ₁ ≤ f (c ₂) < c ₂), then f has a single fixed point, a period two orbit, but no points of period greater than two or f has more than one fixed point but no points of other periods, furthermore, if A≠φ and B≠φ, then f (c ₂) > a (resp. f (c ₁) < b). (2) If f (c ₁) ≤ c ₁ (resp. f (c ₂) ≥ c ₂), then f has more than one fixed point, furthermore, if B≠φ and A\ {a} ≠φ, f (c ₂) ≥ a or if a ₁ < f (c ₂) < a, f ² (c ₂) > f (c ₂), (resp. f has more than one fixed point, furthermore, if A≠φ and B\{b}≠φ, f (c ₁) ≤ b or if b < f (c ₂) < b ₁, f ² (c ₁) < f (c ₁)). (3) If f (c ₁) > c ₂ and f (c ₂) < c ₁, then f has a single fixed point, a single period two orbit lying in I\(u, v) but no points of period greater than two, where u, v ∈ [c ₁, c ₂] such that f (u) = c ₂ and f (v) = c ₁. Supported by the National Natural Science Foundation of China (No. 19961001, No. 60334020) and Outstanding Young Scientist Research Fund. (No. 60125310)     

Molality as a unit of measure for expressing 1H MRS brain metabolite concentrations in vivo

Absolute concentrations of cerebral metabolite in in vivo 1H magnetic resonance spectroscopy studies (1H-MRS) are widely reported in molar units as moles per liter of tissue, or in molal units as moles per kilogram of tissue. Such measurements require external referencing or assumptions as to local water content. To reduce the scan time, avoid assumptions that may be invalid under specific pathologies, and provide a universally accessible referencing procedure, we suggest that metabolite concentrations from 1H-MRS measurements in vivo be reported in molal units as moles per kilogram of tissue water. Using internal water referencing, a two-compartment water model, a simulated brain spectrum for peak identification, and a spectroscopic bi-exponential spin-spin relaxation segmentation technique, we measured the absolute concentrations for the four common 1H brain metabolites: choline (Cho), myo-inositol (mIno), phosphocreatine + creatine (Cr), and N-acetyl-aspartate (NAA), in the hippocampal region (n = 26) and along the Sylvian fissure (n = 61) of 35 healthy adults. A stimulated echo localization method (20 ms echo time, 10 ms mixing time, 4 s repetition time) yielded metabolite concentrations, uncorrected for metabolite relaxation or contributions from macromolecule resonances, that were expectantly higher than with molar literature values. Along the Sylvian fissure the average concentrations (coefficient of variation (CV)) in mmoles/kg of tissue water were 17.6 (12%) for NAA, 14.2 (9%) for Cr, 3.6 (13%) for Cho, and 13.2 (15%) for mIno. Respective values for the hippocampal region were 15.7 (20%), 14.7 (16%), 4.6 (19%), and 17.7 (26%). The concentrations of the two regions were significantly different (p 相似文献