High-Resolution Infrared Spectroscopy of Methyl Isocyanide: The ν3, ν6, and ν7 + ν8 Bands

The vibration-rotation spectrum of methyl isocyanide (CH₃NC) has been recorded with the aid of a high-resolution Fourier transform spectrometer in the region 1370 to 1560 cm⁻¹ containing the perpendicular band of the fundamental vibration ν₆ (species E), the weaker parallel band of the ν₃ (A₁) fundamental, and the perpendicular combination band ν₇ + ν₈ (E) enhanced by Fermi resonance with ν₆. Sixteen hundred seventy well-resolved lines were assigned to 15 subbands of ν₆, 6 subbands of ν₃, and 3 subbands of ν⁻₇ + ν⁻₈. A strong x, y-Coriolis resonance between ν₃ and ν₆ and Fermi resonance between ν^±₆ and the E component ν₇ + ν₈, as well as between ν₃ and the A_1,2 components ν^±₇ + ν₈, greatly affects the spectrum. Additional weaker anharmonic interaction of ν₆ with the ν₄ + 2ν²₈ combination and higher-order rotational interactions connecting the various states were also detected in the spectrum. All of these interactions have been incorporated into a 9 × 9 Hamiltonian matrix used for modeling the upper states of the observed transitions. A set of spectroscopic constants is reported for the upper states of the bands ν₃, ν₆, and ν₇ + ν₈ and for ν₄ + 2ν²₈ which reproduces the observed lines with an overall standard deviation of 0.0012 cm⁻¹.     

The application of cepstral techniques to the measurement of transfer functions and acoustical reflection coefficients

Cepstral processing techniques in principle allow the separation of superposed pulses, such as those which occur in acoustic reflection, where a reflected pulse is a delayed and distorted version of the incident pulse. Additionally, the impulse response of the reflecting system, or equivalently its reflection coefficient, can also be determined. In practice, the accurate extraction of the impulse response is rendered difficult by the mathematical and computational properties of the power cepstrum procedure. In particular, spectral irregularity of the incident pulse, experimental noise and cepstral aliasing can cause the impulse response in the cepstrum to be masked. However, by careful selection of the incident signal, anti-aliasing filter, sampling frequency and echo delay in relation to the total sampling time, and the use of signal processing techniques such as time domain averaging, recursive filtering in the cepstral domain and zero padding, it is possible to produce good quality cepstra in which the reflector impulse response appears as an isolated feature. Experiments conducted on an electrical analogue of the acoustical reflection process have allowed the cepstral technique to be developed and evaluated. The acoustical reflector is simulated by a passive electrical filter network; the objective of the measurement and subsequent processing is the determination of the transfer function of this network. Good agreement is obtained between theoritical and measured transfer functions for a variety of filter networks indicating that cepstral techniques may be useful for acoustical reflection measurements given adequate transducer properties and environmental conditions.     

Complete reducibility and Steinberg endomorphisms

Let G be a connected reductive algebraic group defined over an algebraically closed field of positive characteristic. We study a generalization of the notion of G-complete reducibility in the context of Steinberg endomorphisms of G. Our main theorem extends a special case of a rationality result in this setting.     

Performance analysis of a batch service queue arising out of manufacturing system modelling

In this paper, we present an exact analysis of a queueing system with Poisson arrivals and batch service. The system has a finite numberS of waiting places and a batch service capacityb. A service period is initialized when a service starting thresholda of waiting customers has been reached. The model is denoted accordingly byM/G ^[a,b] /1–S. The motivation for this model arises from manufacturing environments with batch service work stations, e.g. in machines for computer components and chip productions. The method of embedded Markov chain is used for the analysis, whereby a representation of the general service time is obtained via a moment matching approach. Numerical results are shown in order to illustrate the dependency of performance measures on special sets of system parameters. Furthermore, attention is devoted to the issues of starting rules, where performance objectives like short waiting time, small blocking probability and minimal amount of work in progress are taken into account.