Limit cycle analysis of a class of strongly nonlinear oscillation equations

The limit cycle of a class of strongly nonlinear oscillation equations of the form % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiqadwhagaWaaiabgUcaRmXvP5wqonvsaeHbbjxAHXgiofMCY92D% aGqbciab-DgaNjab-HcaOiaadwhacqWFPaqkcqWF9aqpcqaH1oqzca% WGMbGaaiikaiaadwhacaGGSaGabmyDayaacaGaaiykaaaa!50B8!\[\ddot u + g(u) = \varepsilon f(u,\dot u)\] is investigated by means of a modified version of the KBM method, where is a positive small parameter. The advantage of our method is its straightforwardness and effectiveness, which is suitable for the above equation, where g(u) need not be restricted to an odd function of u, provided that the reduced equation, corresponding to =0, has a periodic solution. A specific example is presented to demonstrate the validity and accuracy of our 09 method by comparing our results with numerical ones, which are in good agreement with each other even for relatively large .     

Structures of boron chelates of mono- and diacylketene aminals

The molecular and crystal structures of diphenylboron chelates of acetylketeneN-benzoylaminal and 2-(N-benzoyl)diaminomethylene-4-dimethylaminomethylenecyclohexane-1,3-dione and the structure of the difluoroboron complex of diacetylketeneN-benzoylaminal were established. It was found that the aminovinylcarbonyl fragment of the ligand is involved in the formation of a boron-containing ring. A delocalized -electron system over the NCCCO fragment of the chelate ring is characteristic of the molecules studied both in crystals and solutions.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2541–2546, October, 1996.     

Determination of pyrene and benzo(a)pyrene residues in water by derivative synchronous solid-phase spectrofluorimetry

Benzo(a)pyrene (BaP) and pyrene (Pyr) are two polycyclic aromatic hydrocarbons (PAHs) showing native fluorescence in solution. Both compounds have been determined in water at trace levels by solid-phase spectrofluorimetry, in which BaP and Pyr are fixed on Sephadex G-25 gel and the relative fluorescence intensity is measured after the system is packed in a 1-mm silica cell. First-derivative synchronous spectra obtained at =38 nm were used to determine BaP and Pyr in the presence of other potentially interferent PAHs. The spectral characteristics of the PAHs-gel system are described, the applicable concentration ranges being 0.4–2.5 ng/ml for BaP and 0.7–4.5 ng/ml for Pyr. The relative standard deviations were 1.1% and 1.4% for BaP and Pyr respectively. The detection limits were 0.04 ng/ml for BaP and 0.1 ng/ml for Pyr. The method was applied to the analysis of both compounds in water at trace levels and a recovery study on tap, natural and sea waters was carried out.     

Singularity spectrum of fractal signals from wavelet analysis: Exact results

The multifractal formalism for singular measures is revisited using the wavelet transform. For Bernoulli invariant measures of some expanding Markov maps, the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima. The generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures. It is demonstrated that the Hausdorff dimensionD(h) of the set of singularities of Hölder exponenth can be directly determined from the wavelet transform modulus maxima. The singularity spectrum so obtained is shown to be not disturbed by the presence, in the signal, of a superimposed polynomial behavior of ordern, provided one uses an analyzing wavelet that possesses at leastN>n vanishing moments. However, it is shown that aC behavior generally induces a phase transition in theD(h) singularity spectrum that somewhat masks the weakest singularities. This phase transition actually depends on the numberN of vanishing moments of the analyzing wavelet; its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal. These theoretical results are illustrated with numerical examples. They are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional Brownian motions and turbulent velocity signals.     

用超临界气体抽提方法研究抚顺烟煤的组成和结构——Ⅰ.抽出物的分离及GC、GC/MS分析

将抚顺烟煤用甲苯作溶剂,在半连续抽提装置上,于350℃、20MPa条件下,进行超临界气体抽提。抽出物先分离成油、沥青烯及前沥青烯三个族组份,再用离子交换树脂、硅胶柱色谱作进一步分离。GC和GC/MS的分析结果表明,油段分中存在正构烷烃(C_(13)—C_(31))、类异戊二烯化合物及长链烷基苯系列,这些化合物可提供抚顺烟煤的地球化学信息。     

Electronic control of stereoselectivity. 20. Crystal and molecular structure of the ferrocene derived from tricyclo[5.2.1.02,6]Deca-2,5,8-triene

Reaction of the isodicyclopentadienide anion and its dehydro congener with Fe(II) leads to a stereochemically homogeneous ferrocene derivative in each instance. Through chemical correlation and X-ray analysis, above-plane complexation is established for both halves within the two sandwich compounds.     

Electron microprobe analysis of micro amount powder samples: A case study on high purity coal

For the major, minor and trace element analysis of the inorganic compounds of a Ruhr-Saar coal different preparation techniques are investigated with X-ray fluorescence analysis, electron microprobe and classical wet chemical methods minimizing sample weight at standard preparation times and analytical accuracies. Considering accuracy as well as preparation efforts, determinations by electron microprobe on small sample amounts (<50 mg) proved to be superior to the other methods.Abbreviations AAS atomic absorbtion spectrometry - EMA electron microprobe analysis - IC ion chromatography - ISE ion sensitive electrode - PHOT photometry - WCA wet chemical analysis - XRF X-ray fluorescence analysis - LTA low temperature plasma ashing - HTA high temperature ashing - l.o.i. loss on ignition     

苦味酸荧光光化学传感器在药物分析中的应用

苦味酸水浴液对固定在增塑的聚氯乙烯（ＰＶＣ）膜中的蒽有可逆荧光熄灭作用，据此研制了测定苦味酸的荧光光化学传感器。该传感器的敏感膜的最佳组成为６～８ｍｇ蒽、５０ｍｇＰｖＣ粉、１００ｍｇ邻苯二甲酸二异辛酯。测定苦味酸的浓度范围为３．０４×１０￣（－６）～６．１６×１０￣（－３）ｍｏｌ／Ｌ，重现性良好，响应时间为５～４０秒，该传感器选择性好，许多常见亲脂明离子不干扰测定，可用于药物奎宁及辛可宁的间接测定。     

Flow injection analysis methods for determination of diffusion coefficients

Two flow injection analyses (FIA) methods for the determination of diffusion coefficients in a straight single tube FIA system were developed. Based on the analytical solution of the convection-diffusion equation, linear relationships of the logarithmic values of the dispersion coefficient (D) and the half-peak width (W_1/2) with the diffusion coefficient (D_m) were obtained. Experiments were designed to verify these methods. For example, for potassium hexacyanoferrate (III) a D_m value of 0.72 × 10⁵ cm² s⁻¹ was found versus a literature value of 0.76 × 10⁵ cm² s⁻¹ (error, 5%). For potassium hexacyanoferrate (II) a D_m value of 0.67 × 10⁵ cm² s⁻¹ was obtained versus a literature value of 0.63 × 10⁵ cm² s⁻¹ (error, 6%). The diffusion coefficients of some important biomedical compounds, such as dopamine, epinephrine, norepinephrine and ascorbic acid, were then determined. The values of 10⁵ D_m/cm² s⁻¹ are 0.60 ± 0.03, 0.44 ± 0.02, 0.60 ± 0.01 and 0.68 ± 0.06, respectively.     

示波极谱法测定地质样品中痕量氟

提出了地质样品经半熔法分解后,8-羟基喹啉沉淀干扰组分,过量的8-羟基喹啉用四氯化碳萃取分离,在六次甲基四胺缓冲液中测定Ce(Ⅲ)-ALC-F~-络合吸附波。并对标准物质中F~-进行测定,其测定值与推荐值吻合。方法的RSD为5.6％,检出限为0.6μg·g~(-1)。