Dual Gabor frames: theory and computational aspects

We consider a general method for constructing dual Gabor elements different from the canonical dual. Our approach is based on combining two Gabor frames such that the generated frame-type operator S/sub g,/spl gamma// is nonsingular. We provide necessary and sufficient conditions on the Gabor window functions g and /spl gamma/ such that S/sub g,/spl gamma// is nonsingular for rational oversampling, considering both the continuous-time and the discrete-time settings. In contrast to the frame operator, the operator S/sub g,/spl gamma// is, in general, not positive. Therefore, all results in Gabor analysis that are based on the positivity of the frame operator cannot be applied directly. The advantage of the proposed characterization is that the algebraic system for computing the Gabor dual elements preserves the high structure of usual Gabor frames, leading to computationally efficient algorithms. In particular, we consider examples in which both the condition number and the computational complexity in computing the proposed dual Gabor elements decrease in comparison to the canonical dual Gabor elements.     

Combustion of coffee husks

Combustion mechanisms of two types of coffee husks have been studied using single particle combustion techniques as well as combustion in a pilot-scale fluidised bed facility (FBC), 150 mm in diameter and 9 m high. Through measurements of weight-loss and particle temperatures, the processes of drying, devolatilisation and combustion of coffee husks were studied. Axial temperature profiles in the FBC were also measured during stationary combustion conditions to analyse the location of volatile release and combustion as a function of fuel feeding mode. Finally the problems of ash sintering were analysed. The results showed that devolatilisation of coffee husks (65–72% volatile matter, raw mass) starts at a low temperature range of 170–200°C and takes place rapidly. During fuel feeding using a non water-cooled system, pyrolysis of the husks took place in the feeder tube leading to blockage and non-uniform fuel flow. Measurements of axial temperature profiles showed that during under-bed feeding, the bed and freeboard temperatures were more or less the same, whereas for over-bed feeding, freeboard temperatures were much higher, indicating significant combustion of the volatiles in the freeboard. A major problem observed during the combustion of coffee husks was ash sintering and bed agglomeration. This is due to the low melting temperature of the ash, which is attributed to the high contents of K₂O (36–38%) of the coffee husks.     

Fluidized bed spray granulation: Analysis of the system behaviour by means of dynamic flowsheet simulation

Nowadays, software tools for the flowsheet simulation of industrial processes are commonly used for design, simulation, balancing, troubleshooting and optimization purposes. Most of the tools are applicable to fluid processes only and cannot be effectively used for processes which involve solids.In this contribution we want to present the conceptual design of a new system applicable for the dynamic flowsheet simulation of complex solids processes. This system is developed as an enhancement to the existing simulation program.The novel software is able to simulate the unsteady behaviour of complex circuits of granulation processes. The transient behaviour during the start-up and changing of the process or material parameters can also be examined.As flowsheet examples, a typical spray granulation process with different schemes consisting of fluidized bed granulators, screens, mill and splitters was used. The mathematical model of the fluidized bed granulator is described by a one-dimensional population balance equation and coupled with heat and mass transfer and simple fluid dynamics.Received simulation results have shown that the proposed concept of the dynamic flowsheet simulation of granulation processes can be used effectively and has the potential to be generalized for other types of solids processes.     

Changes in nasal tip projection and rotation after septorhinoplasty: a cephalometric analysis

PURPOSE: This prospective study reports on changes in nasal tip projection and nasal tip rotation before and after septorhinoplasty analyzed cephalometrically. PATIENTS AND METHODS: Forty patients undergoing primary septorhinoplasty were studied prospectively. Lateral cephalometric radiographs taken in the natural head position were obtained before and 6 to 45 months (mean, 17.1) after surgery. In 10 patients, serial radiographs were taken at 6 and 12 months, and in seven patients they were taken at 12 and 24 months after surgery. Nasal tip projection (NTP) was defined as the distance between articulare (Ar) and pronasion (PRN). Nasal tip rotation (NTR) was defined as the change in the angle (N-Ar-PRN) after surgery. A surgical goal to increase, decrease, or maintain NTP and NTR was assigned to each patient before surgery. RESULTS: NTP changed in the desired direction in 16 of 40 patients (40%). NTR changed in the desired direction in 25 of 40 patients (63%). In the patients studied serially, NTP decreased an average 0.7 mm between 6 and 12 months (P = .018), and 0.6 mm between 12 and 24 months (P = .071). CONCLUSIONS: Decreased NTP and NTR were the most easily achieved surgical objectives. Maintaining or increasing NTP is less predictable. Typically, there is a progressive loss of NTP after surgery independent of the surgical goal. Cephalometric analysis is a useful tool to measure changes in NTP and NTR after septorhinoplasty.