Generalized Gabor expansions of discrete-time signals in l2(Z) via biorthogonal-like sequences

In this paper, a biorthogonal-like sequences (BLS) theory and its application to the generalized Gabor expansions (equivalently, the generalized short-time Fourier transform/filterbank summation) are presented. A pair of BLS's are defined to be two sequences satisfying a biorthogonal-like condition (BLC), which is a moment equation and equivalent to a linear difference equation. We show that two collections in a Hilbert space generated by a pair of BLS's in the joint time-frequency domain are complete, either can be used as an analysis filter, and the other can be used as a synthesis filter for a generalized Gabor expansion of discrete-time signals. A sufficient and necessary condition on the existence of BLS's based on the moment equation is presented, which is simpler to use than frame theory. Given a filter generating a frame, its BLS's also generate frames. The dual frame is one of them. Given a FIR analysis/synthesis filter, there is a FIR synthesis/analysis filter if BLS's exist. The algorithm to compute FIR analysis and synthesis filters based on the linear difference equation is presented in this paper, which is simpler than frame operator     

Partially hidden Markov models

Partially hidden Markov models (PHMM) are introduced. They differ from the ordinary HMMs in that both the transition probabilities of the hidden states and the output probabilities are conditioned on past observations. As an illustration they are applied to black and white image compression where the hidden variables may be interpreted as representing noncausal pixels     

Statistical computer-aided design for microwave circuits

A useful methodology for microwave circuit design is presented. A statistical technique known as Design of Experiments is used in conjunction with computer-aided design (CAD) tools to obtain simple mathematical expressions for circuit responses. The response models can then be used to quantify response trade-offs, optimize designs, and minimize circuit variations. The use of this methodology puts the designer's intelligence back into design optimization while making “designing for circuit manufacturability” a more systematic and straightforward process. The method improves the design process, circuit performance, and manufacturability. Two design examples are presented in context to the new design methodology     

Bayes and classical estimation of environmental factors for thebinomial distribution

An environmental factor converts reliability test results at one environmental condition into equivalent “failure” information at other environments. This paper studies environmental-factor estimation for the binomial distribution. Under general conditions, Bayes point estimates and credibility limits for environmental factors are derived. Classical point and confidence interval estimates are introduced and compared with the Bayes estimators. The characteristics of Bayes and classical estimators for the binomial distribution are summarized through numerical computation and theoretical analysis. A numerical example of reliability assessment by means of environmental factors is presented     

Approximate sine-Gordon solitons

We look at the recently proposed scheme of approximating a sine-Gordon soliton by an expression derived from two dimensional instantons. We point out that the scheme of Sutcliffe in which he uses two dimensional instantons can be generalised to higher dimensions and that these generalisations produce even better approximations than the original approximation. We also comment on generalisations to other models.     

Multiresolution segmentation of respiratory electromyographicsignals

Analysis of respiratory electromyographic (EMG) signals in the study of respiratory control requires the detection of burst activity from background (signal segmentation), and focuses upon the determination of onset and cessation points of the burst activity (boundary estimation). The authors describe a new automated multiresolution technique for signal segmentation and boundary estimation. During signal segmentation, a new transitional segment is defined which contains the boundary between background a burst activity. Boundary estimation is then performed within this transitional segment. Boundary candidates are selected and a probability is attributed to each candidate, using an artificial neural network. The final boundary for a given transitional segment is the boundary estimate with the maximum a posteriori probability. This new method has proved accurate when compared to boundaries chosen by two investigators     

Time-marching numerical schemes for the electric field integral equation on a straight thin wire

We derive and analyse four algorithms for computing the current induced on a thin straight wire by a transient electric field. They all involve solving the thin wire electric field integral equations (EFIEs) and consist of a very accurate differential equations solver together with various schemes to approximate the vector potential integral equation. We carry out a rigorous numerical stability analysis of each of these methods. This has not previously been done for solution schemes for the thin wire EFIEs. Each scheme is shown to be stable and convergent provided the radius of the wire is small enough for the thin wire equations to be a valid model.     

Molecular addressing? Studies on light-induced reorientation in liquid-crystalline side chain polymers

Polarized light leads to an effective reorientation of the optic axis in the glassy state of liquid-crystalline side chain polymers containing azobenzene mesogenic groups, via a trans-cis and cis-trans isomerization. Using a combination of U V and IR dichroitic studies it is shown for copolymers consisting of chromophores (azobenzene) and non-chromophores (phenylbenzoate) that only the chromophores are reoriented by light as far as the glassy state is concerned. Individual chromophores are thus addressed by photoselection. Photoselection in the fluid nematic state, on the other hand, leads also to a reorientation of the non-chromophores.     

A shock tube study of the reaction of methyl radicals with hydroxyl radicals

The reaction of CH₃ with OH has been studied near 1200 K and 1 atmosphere pressure in shock tube experiments in which UV absorption was used to monitor [OH]. A rate coefficient of (1.1 ± 0.3) × 10¹³ cm³/mol-s was measured for removal of OH by CH₃. This measured value is compared with previous experimental data and calculations. Several possible reaction channels are discussed, and although products were not monitored, it seems probable, on the basis of other work and theoretical estimates, that the primary mechanism (?75%) for the removal of OH by CH₃ at these conditions is their combination to form CH₃OH. Rate coefficients of (5.3 ± 0.8) × 10¹² and (9.0 ± 1.4) × 10¹² cm³/mol-s were measured for the reactions of OH with acetone and ethane, respectively, at the same temperature and pressure.     

Inclusive (γ, N), (γ, NN) and (γ, Nπ) reactions in nuclei at intermediate energies

Differential cross sections of nucleons excited in photonuclear reactions in medium and heavy nuclei are studied by considering all relevant reaction mechanisms leading to the excitation of protons or neutrons. We take advantage of previous microscopic studies for the absorption and scattering of photons and photoproduced pions, and implement a simulation code in order to take into account the propagation of the nucleons as well as their collisions with other nucleons in the nuclear medium, which generate secondary excited nucleons. Comparison with experimental data is done. Cross sections for nucleon emission in coincidence with one pion are also calculated, and some coincidence observables are discussed.