Small compact perturbation of strongly irreducible operators

An operatorT onH is called strongly irreducible ifT is not similar to any reducible operators. In this paper, we shall say yes to answer the following question raised by D. A. Herrero.Given an operatorT with connected spectrum (T) and a positive number , can we find a compact operatorK with K < such thatT+K is strongly irreducible?Supported by National Natural Science Foundation of China(19901011), Mathematical Center of State Education Commission of China and 973 Project of China     

On pointwise estimate for Gamma operators

For linear combinations of Gamma operators, if 0＜a＜2r, 1/2-1/2r≤λ≤l, or 0≤λ＜1/2-1/2r(r≥2),0＜a＜r+10＜a<(r+1)/1-λ, we obtain an equivalent theorem with ωuλρ(f ,t) instead of ωrλφ(f,t), where ωuφ(f,t) is theDitzian-Totik moduli of smoothness.     

New Wavelet Bases and Isometric Between Symbolic Operators Spaces $$ {\text{OP}}S^{m}_{{1,\delta }} $$ and Kernel Distributions Spaces

In the fifties, Calderón established a formal relation between symbol and kernel distribution, but it is difficult to establish an intrinsic relation. The Calderón-Zygmund (C-Z) school studied the C-Z operators, and Hörmander, Kohn and Nirenberg, et al. studied the symbolic operators. Here we apply a refinement of the Littlewood-Paley (L-P) decomposition, analyse under new wavelet bases, to characterize both symbolic operators spaces \({\text{OP}}S^{m}_{{1,\delta }} \) and kernel distributions spaces with other spaces composed of some almost diagonal matrices, then get an isometric between \({\text{OP}}S^{m}_{{1,\delta }} \) and kernel distribution spaces     

Synthesis of single crystal BaWO4 nanowires in catanionic reverse micelles

High aspect-ratio, single crystal BaWO4 nanowires with diameters as small as 3.5 nm and lengths up to more than 50 microns were synthesized in catanionic reverse micelles formed by an equimolar mixture of two surfactants: undecylic acid and decylamine.     

Synthesis and reversible thermo-induced conformational transitions of a stable nitroxide biradical based on calix[4]arene

A stable paramagnetic calix[4]arene(III) bearing two nitroxide groups on the upper rim is synthesized, which exhibits a strong intramolecular spin-spin exchange interaction and is found to be able to undergo reversible conformational transitions upon heating.     

Functionalization of monofluoroallene and the synthesis of aryl-substituted conjugated fluorodienes

[reaction: see text] 4-Fluoroallenol 3a, prepared from 1, cyclized easily to 4 but preserved its fluoroallenyl integrity under oxidation and S(N)2 displacement to yield aldehyde, amine, mesylate, and halide 6. Allylic isomerization yielded 2-halo-1-fluoro-1,3-butadiene 7, which underwent a Suzuki coupling to give aryl-substituted conjugated diene 8.     

Measurement of B0-B-0 flavor oscillations in hadronic B0 decays

Flavor oscillations of neutral B mesons have been studied in e+e- annihilation data collected with the BABAR detector at center-of-mass energies near the upsilon(4S) resonance. The data sample used for this purpose consists of events in which one B0 meson is reconstructed in a hadronic decay mode, while the flavor of the recoiling B0 is determined with a tagging algorithm that exploits the correlation between the flavor of the heavy quark and the charges of its decay products. From the time development of the observed mixed and unmixed final states, we determine the B0-B-0 oscillation frequency deltamd to be 0.516+/-0.016(stat)+/-0.010(syst) ps-1.     

Measurement of B --> K*gamma branching fractions and charge asymmetries

The branching fractions of the exclusive decays B0-->K(*0)gamma and B+-->K(*+)gamma are measured from a sample of (22.74+/-0.36)x10(6) BB decays collected with the BABAR detector at the PEP-II asymmetric e(+)e(-) collider. We find B (B0-->K(*0)gamma) = [4.23+/-0.40(stat)+/-0.22(syst)]x10(-5), B(B+-->K(*+)gamma) = [3.83+/-0.62(stat)+/-0.22(syst)]x10(-5) and constrain the CP-violating charge asymmetry to be -0.170K(*)gamma)<0.082 at 90% C.L.     

Broadband waveguide intersections with low cross talk in photonic crystal circuits

We propose a new mechanism for constructing waveguide intersections with broad bandwidth and low cross talk in photonic crystal (PC) circuits. The intersections are created by combination of coupled-cavity wave-guides (CCWs) with conventional line-defect waveguides. This mechanism utilizes the strong dependence of the defect coupling on the field pattern in the defects and the alignment of the defects (i.e., the coupling angle) in CCWs. By properly designing the defect mode, we demonstrate through numerical simulation the establishment of such a waveguide intersection in one of the most useful PCs, which is based on a two-dimensional triangular lattice of air holes made in a dielectric material. The transmission of a 500-fs pulse at ~1.3 microm is simulated by use of the finite-difference time-domain method, showing negligible distortion and low cross talk.     

Spatial vector solitons consisting of counterpropagating fields

We present the experimental observation of a spatial vector soliton formed by counterpropagation of coherent optical fields. This is to our knowledge the first observation of a vector soliton in which the induced waveguide (potential) is periodic in the propagation direction. This vector soliton induces a waveguide and a thick grating within the waveguide, which can be used as a tunable optical waveguide filter.