Wavelet-Based Method for Time-Domain Noise Analysis and Reduction in a Frequency-Scan Ion Trap Mass Spectrometer

We adopt an orthogonal wavelet packet decomposition (OWPD) filtering approach to cancel harmonic interference noises arising from an AC power source in time domain and remove the resulting rf voltage interference noise from the mass spectra acquired by using a charge detection frequency-scan quadrupole ion trap mass spectrometer. With the use of a phase lock resampling technique, the transform coefficients of the rf interference in signals become a constant, exhibiting a shift of the baseline in different rf phases. The rf interference is therefore removable by shifting the baselines back to zero in OWPD coefficients. The approach successfully reduces the time-domain background noise from 1367 electrons (rms) to 408 electrons (rms) (an improvement of 70?%) and removes the high frequency noise components in the charge detection ion trap mass spectrometry. Unlike other smoothing or averaging methods commonly used in the mass-to-charge (m/Ze) domain, our approach does not cause any distortion of original signals.     

Low molecular weight organogelators derived from threefold symmetric tricarbamates

A group of new low molecular weight organogelators based on threefold symmetric tricarbamate were synthesized and characterized. The tricarbamates with long alkyl chains were able to gelate a wide range of polar and nonpolar organic solvents such as acetonitrile and cyclohexane, generally at concentrations lower than 20 g/L. The best organogel formation was obtained using a threefold symmetric tricarbamate in n-dodecane, in which a sufficiently transparent gel was formed at the critical gelation concentration 1 g/L. Intermolecular hydrogen bonding by the tricarbamate in a nonpolar solvent benzene-d₆ was indicated by ¹H NMR spectra. Its maximum UV absorption was 11 nm higher in chloroform than in n-dodecane, and this red shift indicated increased conjugation between the benzene core and the carbamate substituents, which confirmed a change in its conformation from nonpolar to polar solvent. The self-assembling behavior of the tricarbamate in dilute solutions was investigated by TEM. Fiber-like networks were observed in a large range of solution concentrations.     

Reactive resonance in a polyatomic reaction

In the course of an extensive investigation aimed at understanding the detailed mechanisms of a prototypical polyatomic reaction, several remarkable observations were uncovered. To interpret these findings, we surmise the existence of a reactive resonance in this polyatomic reaction. The reaction of concern is F+CH4-->HF+CH3, and the abnormal attributes were revealed only near the reaction threshold. The discovery of reactive resonance in a polyatomic reaction is more than just an extension from a typical atom+diatom reaction. As shown here, it holds great promise to disentangle the elusive intramolecular vibrational dynamics of transient collision complex in the critical transition-state region.     

On Some Three-Color Ramsey Numbers

 In this paper we study three-color Ramsey numbers. Let K _i,j denote a complete i by j bipartite graph. We shall show that (i) for any connected graphs G ₁, G ₂ and G ₃, if r(G ₁, G ₂)≥s(G ₃), then r(G ₁, G ₂, G ₃)≥(r(G ₁, G ₂)−1)(χ(G ₃)−1)+s(G ₃), where s(G ₃) is the chromatic surplus of G ₃; (ii) (k+m−2)(n−1)+1≤r(K _1,k , K _1,m , K _n )≤ (k+m−1)(n−1)+1, and if k or m is odd, the second inequality becomes an equality; (iii) for any fixed m≥k≥2, there is a constant c such that r(K _k,m , K _k,m , K _n )≤c(n/logn), and r(C _2m , C _2m , K _n )≤c(n/logn) ^m/(m−1) for sufficiently large n. Received: July 25, 2000 Final version received: July 30, 2002 RID="*" ID="*" Partially supported by RGC, Hong Kong; FRG, Hong Kong Baptist University; and by NSFC, the scientific foundations of education ministry of China, and the foundations of Jiangsu Province Acknowledgments. The authors are grateful to the referee for his valuable comments. AMS 2000 MSC: 05C55     

<Emphasis Type="Italic">k</Emphasis>-factors in regular graphs

Plesnik in 1972 proved that an （m - 1）-edge connected m-regular graph of even order has a 1-factor containing any given edge and has another 1-factor excluding any given m - 1 edges. Alder et al. in 1999 showed that if G is a regular （2n ＋ 1）-edge-connected bipartite graph, then G has a 1-factor containing any given edge and excluding any given matching of size n. In this paper we obtain some sufficient conditions related to the edge-connectivity for an n-regular graph to have a k-factor containing a set of edges and （or） excluding a set of edges, where 1 ≤ k ≤n/2. In particular, we generalize Plesnik＇s result and the results obtained by Liu et al. in 1998, and improve Katerinis＇ result obtained 1993. Furthermore, we show that the results in this paper are the best possible.     

One-pot conditional self-assembly of multicopper metallacycles

The self-assembly of supramolecular metallacycles via the coordination-driven directional bonding approach can be modified to produce some unexpected structural variations. The combination of a flexible ligand-capped dinuclear transition-metal acceptor like [Cu(2)(dppm)(2)(NCMe)(2)]X(2) (1X(2); dppm = Ph(2)PCH(2)PPh(2); X(-) = BF(4)(-), PF(6)(-), or BPh(4)(-)) with monodentate-bidentate donors like 2-, 3-, and 4-pyridylcarboxylates produced oligomeric compounds [{Cu(2)(dppm)(2)}(μ-(2-PyCO(2)))](2)X(2) (2X(2)), [{Cu(2)(dppm)(2)}(μ-(3-PyCO(2)))](2)X(2) (3X(2)), and [{Cu(2)(dppm)(2)}(μ-(4-PyCO(2)))](4)X(4) (4X(4)), respectively, as the thermodynamically stable products in one-pot reactions. However, the modified self-assembly is still subject to steric hindrance. The reaction of complex 1(BF(4))(2) with 6-Me-3-PyCO(2)H did not produce a polygonal dimeric metallacycle but a simple dinuclear complex, [Cu(2)(dppm)(2)(6-Me-3-PyCO(2))](BF(4)) (5(BF(4))). The crystal structures of complexes 2(PF(6))(2), 3(PF(6))(2), 4(BF(4))(4), and 5(BF(4)) were determined using X-ray diffraction.     

Hybrid cable television and orthogonal-frequency-division-multiplexing transport system basing on single wavelength polarization and amplitude remodulation schemes

A hybrid community antenna television (CATV) and orthogonal-frequency-division-multiplexing (OFDM) transport system is proposed and experimentally demonstrated to transmit multiple CATV channels and bi-directional radio frequency signals on a single optical carrier. By polarization remodulating an optical CATV signal with downstream OFDM signals and then amplitude remodulating upstream OFDM signals with the hybrid CATV/OFDM signals, this architecture can efficiently utilize only one optical carrier to support optical analog/digital CATV transmission and bi-directional wireless broadband services for each client. Good experimental results prove that this architecture provides a proper wavelength utilization scheme for future multiwavelength optical transport systems.