A time-domain test for some types of nonlinearity

The bispectrum and third-order moment can be viewed as equivalent tools for testing for the presence of nonlinearity in stationary time series. This is because the bispectrum is the Fourier transform of the third-order moment. An advantage of the bispectrum is that its estimator comprises terms that are asymptotically independent at distinct bifrequencies under the null hypothesis of linearity. An advantage of the third-order moment is that its values in any subset of joint lags can be used in the test, whereas when using the bispectrum the entire (or truncated) third-order moment is required to construct the Fourier transform. In this paper, we propose a test for nonlinearity based upon the estimated third-order moment. We use the phase scrambling bootstrap method to give a nonparametric estimate of the variance of our test statistic under the null hypothesis. Using a simulation study, we demonstrate that the test obtains its target significance level, with large power, when compared to an existing standard parametric test that uses the bispectrum. Further we show how the proposed test can be used to identify the source of nonlinearity due to interactions at specific frequencies. We also investigate implications for heuristic diagnosis of nonstationarity.

Competitive charge-remote and anion-induced fragmentations of the non-8-enoate anion. A charge-remote reaction which co-occurs with hydrogen scrambling

The non-8-enoate anion undergoes losses of the elements of C3H6, C4H8 and C6H12 on collisional activation, The mechanisms of these processes have been elucidated by a combination of product ion and labelling (H-2 and C-13) studies, together with a neutralisation reionisation mass spectrometric study. These studies allow the following conclusions to be made. (i) The loss of C3H6 involves cyclisation of the enolate anion of non-8-enoic acid to yield the cyclopentyl carboxylate anion and propene. (ii) The loss of 'C4H8' is a charge-remote process (one which proceeds remote from the charged centre) which yields the pent-4-enoate anion, butadiene and dihydrogen. This process co-occurs and competes with complex H scrambling. (iii) The major loss of 'C6H12' occurs primarily by a charge-remote process yielding the acrylate anion, hexa-1,5-diene and dihydrogen, but in this case no H scrambling accompanies the process. (iv) It is argued that the major reason why the two charge-remote processes occur in preference to anion-induced losses of but-l-ene and hex-l-ene from the respective 4- and 2-anions is that although these anions are formed, they have alternative and lower energy fragmentation pathways than those involving the losses of but-l-ene and hex-l-ene; viz. the transient 4-anion undergoes facile proton transfer to yield a more stable anion, whereas the 2-(enolate) anion undergoes preferential cyclisation followed by elimination of propene [see (i) above].

The loss of CO from the ortho, meta and para forms of deprotonated methyl benzoate in the gas phase

The ortho, meta and para anions of methyl benzoate may be made in the source of a mass spectrometer by the S(N)2(Si) reactions between HO- and methyl (o-, m-, and p-trimethylsilyl)benzoate respectively. All three anions lose CO upon collisional activation to form the ortho anion of anisole in the ratio ortho>>meta > para. The rearrangement process is charge directed through the ortho anion. Theoretical calculations at the B3LYP/6-311++G(d,p)//HF/6-31+G(d) level of theory indicate that the conversion of the meta and para anions to the ortho anion prior to loss of CO involve 1,2-H transfer(s), rather than carbon scrambling of the methoxycarbonylphenyl anion. There are two mechanisms which can account for this rearrangement, viz. (A) cyclisation of the ortho anion centre to the carbonyl group of the ester to give a cyclic carbonyl system in which the incipient methoxide anion substitutes at one of the two equivalent ring carbons of the three membered ring to yield an intermediate which loses CO to give the ortho anion of anisole, and (B) an elimination reaction to give an intermediate benzyne-methoxycarbonyl anion complex in which the MeOCO- species acts as a MeO- donor, which then adds to benzyne to yield the ortho anion of anisole. Calculations at the B3LYP/6-311++G(d,p)//HF/6-31+G(d) level of theory indicate that (i) the barrier in the first step (the rate determining step) of process A is 87 kJ mol(-1) less than that for the synchronous benzyne process B, and (ii) there are more low frequency vibrations in the transition state for benzyne process B than for the corresponding transition state for process A. Stepwise process A has the lower barrier for the rate determining step, and the lower Arrhenius factor: we cannot differentiate between these two mechanisms on available evidence.

Conversion of linear to rhombic C-4 in the gas phase: A joint experimental and theoretical study

Charge reversal (CR) and neutralization reionization (NR) experiments carried out on a 4-sector mass spectrometer demonstrate that isotopically labeled, linear C-4 anion rearranges upon collisional oxidation. The cations and neutrals formed in these experiments exhibit differing degrees of isotopic scrambling in their fragmentation patterns, indicative of (at least) partial isomerization of both states. Theoretical studies, employing the CCSD(T)/aug-cc-pVDZ//B3LYP/6-31G(d) level of theory, favor conversion to the rhombic C-4 isomer on both cationic and neutral potential-energy surfaces with the rhombic structures predicted to be slightly more stable than the linear forms in each case. The combination of experiment with theory indicates that the elusive rhombic C-4 is formed as a cation and as a neutral following charge stripping of linear C-4(-)

Syntheses of NCN and NC3N from ionic precursors in the gas phase and an unusual rearrangement of neutral NC3N : A joint experimental and theoretical study

Neutral NCN is made in a mass spectrometer by charge stripping of NCN-., while neutral dicyanocarbene NCCCN can be formed by neutralization of either the corresponding anionic and cationic species, NCCCN-. and NCCCN+.. Theoretical calculations at the RCCSD(T)/aug-cc-pVTZ//B3LYP/6-31+G(d) level of theory indicate that the (3)Sigma (-)(g) State of NCCCN is 18 kcal mol(-1) more stable than the (1)A(1) state. While the majority of neutrals formed from either NCCCN-. or NCCCN+. correspond to NCCCN, a proportion of the neutral NCCCN molecules have sufficient excess energy to effect rearrangement, as evidenced by a loss of atomic carbon in the neutralization reionization (NR) spectra of either NCCCN+. and NCCCN-.. C-13 labeling studies indicate that loss of carbon occurs statistically following or accompanied by scrambling of all three carbon atoms. A theoretical study at the B3LYP/6-31+G(d)//B3LYP/6-31+G(d) level of theory indicates that C loss is a consequence of the rearrangement sequence NCCCN --> CNCCN --> CNCNC and that C scrambling occurs within singlet CNCCN via the intermediacy of a four-membered C-2v-symmetrical transition structure.

The gas-phase reaction between silylene and 2-butyne: kinetics, isotope studies, pressure dependence studies and quantum chemical calculations

Time-resolved kinetic studies of the reactions of silylene, SiH2, and dideutero-silylene, SiD2, generated by laser. ash photolysis of phenylsilane and phenylsilane-d(3), respectively, have been carried out to obtain rate coefficients for their bimolecular reactions with 2-butyne, CH3C CCH3. The reactions were studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas at five temperatures in the range 294-612 K. The second-order rate coefficients, obtained by extrapolation to the high pressure limits at each temperature, fitted the Arrhenius equations where the error limits are single standard deviations: log(k(H)(infinity)/cm(3) molecule(-1) s(-1)) = (-9.67 +/- 0.04) + (1.71 +/- 0.33) kJ mol(-1)/RTln10 log(k(D)(infinity)/cm(3) molecule(-1) s(-1)) = (-9.65 +/- 0.01) + (1.92 +/- 0.13) kJ mol(-1)/RTln10 Additionally, pressure-dependent rate coefficients for the reaction of SiH2 with 2-butyne in the presence of He (1-100 Torr) were obtained at 301, 429 and 613 K. Quantum chemical (ab initio) calculations of the SiC4H8 reaction system at the G3 level support the formation of 2,3-dimethylsilirene [cyclo-SiH2C(CH3)=C(CH3)-] as the sole end product. However, reversible formation of 2,3-dimethylvinylsilylene [CH3CH=C(CH3)SiH] is also an important process. The calculations also indicate the probable involvement of several other intermediates, and possible products. RRKM calculations are in reasonable agreement with the pressure dependences at an enthalpy value for 2,3-dimethylsilirene fairly close to that suggested by the ab initio calculations. The experimental isotope effects deviate significantly from those predicted by RRKM theory. The differences can be explained by an isotopic scrambling mechanism, involving H - D exchange between the hydrogens of the methyl groups and the D-atoms in the ring in 2,3-dimethylsilirene-1,1-d(2). A detailed mechanism involving several intermediate species, which is consistent with the G3 energy surface, is proposed to account for this.

Condensed phase combustion travelling waves with sequential exothermic or endothermic reactions

The one-dimensional propagation of a combustion wave through a premixed solid fuel for two-stage kinetics is studied. We re-examine the analysis of a single reaction travelling-wave and extend it to the case of two-stage reactions. We derive an expression for the travelling wave speed in the limit of large activation energy for both reactions. The analysis shows that when both reactions are exothermic, the wave structure is similar to the single reaction case. However, when the second reaction is endothermic, the wave structure can be significantly different from single reaction case. In particular, as might be expected, a travelling wave does not necessarily exist in this case. We establish conditions in the limiting large activation energy limit for the non-existence, and for monotonicity of the temperature profile in the travelling wave.

Speaker identification using higher order spectral phase features and their effectiveness vis-a-vis Mel-Cepstral features

The effectiveness of higher-order spectral (HOS) phase features in speaker recognition is investigated by comparison with Mel Cepstral features on the same speech data. HOS phase features retain phase information from the Fourier spectrum unlikeMel–frequency Cepstral coefficients (MFCC). Gaussian mixture models are constructed from Mel– Cepstral features and HOS features, respectively, for the same data from various speakers in the Switchboard telephone Speech Corpus. Feature clusters, model parameters and classification performance are analyzed. HOS phase features on their own provide a correct identification rate of about 97% on the chosen subset of the corpus. This is the same level of accuracy as provided by MFCCs. Cluster plots and model parameters are compared to show that HOS phase features can provide complementary information to better discriminate between speakers.