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1.
2.
The number of limit cycles for three dimensional Lotka–Volterra systems is an open problem. Recently, Yu et al. (2016) constructed some examples with the possibility of the existence of four limit cycles. Unfortunately, multiple limit cycles are not visible by numerical simulations, because all of them are very close to the interior equilibrium and extremely small. We present a concrete example with multiple limit cycles for three dimensional Lotka–Volterra systems which we can confirm them by numerical simulations. First we prepare the modified formula to compute coefficients of the normal form for the generalized Hopf bifurcation. Applying this formula to three dimensional Lotka–Volterra competitive systems with the aid of the computer algebra system, we derive the critical parameter values explicitly such that the interior equilibrium is exactly an unstable weak focus. Also we show that the heteroclinic cycle on the boundary of R+3 is repelling. This implies that there exists a stable limit cycle by the Poincare–Bendixson theorem. Then, adding some suitable perturbations to parameters, we generate additional two limit cycles near the interior equilibrium by the generalized Hopf bifurcation. Finally we confirm that there exist three limit cycles by numerical simulations.  相似文献   
3.
The introduction of a 1,3-propanediamine unit at the 3-position of (S)-BINOL using a methylene spacer led to the formation of a chiral bifunctional organocatalyst for the aza-Morita–Baylis–Hillman (aza-MBH) reaction. The organocatalyst 1k mediated aza-MBH transformations with high chemical yields and with up to 82% ee.  相似文献   
4.
A confocal micro‐X‐ray fluorescence (micro‐XRF) instrument equipped with a vacuum chamber was newly developed. The instrument is operated under a vacuum condition to reduce the absorption of XRF in the atmosphere. Thin metal layers were developed to evaluate the confocal volume, corresponding to depth resolution. A set of thin metal layers (Al, Ti, Cr, Fe, Ni, Cu, Zr, Mo, and Au) was prepared by a magnetron sputtering technique. The depth resolutions of the new instrument were varied from 56.0 to 10.9 µm for an energy range from 1.4 to 17.4 keV, respectively. The lower limit of detection (LLD) was estimated by comparison with a glass standard reference material NIST SRM 621). The LLDs obtained by a conventional micro‐XRF were compared with the LLDs obtained by a confocal micro‐XRF instrument. The LLDs were improved in the measurement under confocal configuration because of the reduction of background intensity. Finally, layered materials related to forensic investigation were measured. The confocal micro‐XRF instrument was able to nondestructively obtain the distribution of light elements that cannot be detected by measurement in air. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   
5.
The well-known Heun equation has the form
ll{Q(z)\frac d2dz2+P(z)\fracddz+V(z)}S(z)=0,\begin{array}{ll}\left\{Q(z)\frac {d^2}{dz^2}+P(z)\frac{d}{dz}+V(z)\right\}S(z)=0,\end{array}  相似文献   
6.
Prochiral sulfides reacted with Phl=NTs in the presence of a catalytic amount of Cu(I) salt together with a chiral 4,4′-disubstituted bis(oxazoline) ligand to afford the corresponding chiral sulfimides.  相似文献   
7.
Asymmetric intramolecular selenocyclisation of alkenoic acids, alkenols and alkenyl urethanes using chiral ferrocenylselenenyl cations proceeds smoothly to give the corresponding lactones, cyclic ethers and N-heterocyclic compounds, respectively, in moderate yields with very high diastereoselectivities.  相似文献   
8.
Abstract

Protons in alkaline-earth phosphate glasses give much higher mobility than those in silicate glasses. This is caused by the difference in O-H bonding state. Protons in P-OH form a strong hydrogen bonding with oxygen anion, resulting in formation of weak O-H bond.

The electrical conductivity of the glasses is proportional to the square of the proton concentration. The activation energy for the conduction is related to νOH, peak wavenumber of infrared absorption band (around~3000 cm?1), due to fundamental O-H stretching vibration. The mobility of protons increases with decreasing νOH, which depends on the species of ions included in the phosphate glasses.  相似文献   
9.
We describe the synthesis and electronic properties of ladder oligomers of poly(m-aniline) that may be considered as derivatives of azaacenes with cross-conjugated π-systems. Syntheses of ladder oligo(m-aniline)s with 9 and 13 collinearly fused six-membered rings employed Pd-catalyzed aminations and Friedel-Crafts-based ring closures. Structures were confirmed by either X-ray crystallography or correlations between DFT-computed and experimental spectroscopic data such as (1)H, (13)C, and (15)N NMR chemical shifts and electronic absorption spectra. All compounds have planar "azaacene" moieties. The experimental band gaps E(g) ≈ 3.5-3.65 eV, determined by the UV-vis absorption onsets, were in agreement with the TD-DFT-computed vertical excitation energies to the S(1) state. Fluorescence quantum yields of up to 20% were found. Electrochemically estimated HOMO energies of -4.8 eV suggested propensity for a facile one-electron oxidation and just sufficient environmental stability toward oxygen (O(2)). For two oligomers with "tetraazanonacene" moieties, potentials of E(4+/3+) ≈ 1.6-1.7 V vs SCE were determined for four-electron oxidation to the corresponding tetraradical tetracations.  相似文献   
10.
A new numerical method for performing the Nahm transform for charge k=2 caloron is presented. The Weyl equations with boundary impurities are solved directly and the determination of the appropriate basis to the linear system is established. The action densities of the 2-calorons with 10 moduli parameters are shown.  相似文献   
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