Modal reduction

The basic strategy of modal reduction approaches is to retain only certain modes of the high-order model in the low-order model. Wilson et al. (1974) summarized these techniques and showed that many of the published modal approaches are equivalent since they produce identical reduced models. Bonvin (1980) also provides a comparison of the various modal techniques with respect to their steady-state and dynamic accuracies as well as to the dependence of the reduced models on the retained state variables. 

According to Gould (1969), the central theme in modal reduction and control is... 

This basic approach is really divided into several distinct categories. Two of these, Davison s method and Marshall s method, provide suitable modal reduction for the state-space representation of the methanation reactor to a 12th-order model. Comparisons of the models and discussion of additional model reduction are presented in the next section. 

It is evident that, of the 30 modes of the full linear model (with N = 6), 18 are very fast in comparison to the remaining 12 (by 2 orders of magnitude or more). Thus direct modal reduction to a 12th-order model using Davison s method should provide good dynamic accuracy. However, by simply neglecting the non-dominant modes of the system, the contribution of these modes is also absent at steady state, thus leading to possible (usually minor) steady-state offset. Several identical modifications (Wilson et al, 1974) to Davison s... 

FEM or FDM uses these nodal matrices in principle, but their dimension is highly correlated to the level of the model s discretization. With fine discretization, the dimension of the matrices becomes huge. Therefore, the calculation of stability will be very time-consuming. Furthermore, the determination of stability lobe diagrams only requires a fraction of all information within the FEM or FDM the dynamic compliance of the TCP. Under this premise, the dimension of the model is usually reduced with a so-called modal reduction, which encompasses the following steps ... 

Reducing the system of equations with a modal reduction... 

Reduce and simplify the structural model, e.g., by modal reduction (Clough and Penzien 1993) or proper orthogonal decomposition (Earner and Bucher 2012). 

The expected outcomes of the patient may include an optimal response to therapy, management of common adverse reactions, a reduction in anxiety, and an understanding of the prescribed treatment modalities. 

However, the applications of the phenomenon of the modal transition are not limited to the chemical sensing field. Indeed, cladding etching and an HRI layer of sputtered indium tin oxide were exploited to achieve an LPG-based tunable filter with a large tuning range and with limited reduction in the loss peak65. 

The plot of the diameter vs the relative number of pores also provides useful information on the size distribution. A broadening of the size distribution will then give a reduction of the peak height. In contrast to the hexane system, no bi-modal distribution is detected up to the solubility limit of cyclohexane at 25 wt %. 

The latter point is rather critical. In fact, whereas long xr values can be easily attained through a proper choice of the macromolecular system and the binding modality, it may not be an easy task to keep the relaxometric properties of the paramagnetic moiety unaltered, upon formation of the macromolecular adduct. In fact, this may result in a reduced hydration of the Gd(III) ion as donor groups such as aspartate or glutamate on the surface of a protein can replace coordinated water molecules (103 104). When the hydration state is maintained, the occurrence of a marked reduction of the exchange rate of inner-sphere water is very common (see next Section). 

The initial combination modality clinical studies with cisplatin and fractionated radiation therapy was carried out in head and neck cancer with weekly cisplatin (120-160 mg/m2) and conventional single daily fraction radiation (95). In a follow-up intergroup study, patients were randomized to radiation therapy alone or to radiation therapy plus 20 mg/ m2/wk cisplatin (96). Both studies showed no major increase in normal tissue toxicity in the radiation field and showed an increase in response rate. There was no increase in complete response rate or in survival. Bachaud et al.(97) carried out a randomized study comparing radiation therapy alone with concurrent cisplatin (50 mg/m2) and radiation therapy in postoperative patients. This trial produced a significant reduction in local recurrence and improved disease-free survival with 59% of the patients receiving the full planned dose of cisplatin. 

The effectiveness of various therapeutical modalities of supplemental vitamin A has been examined in numerous studies using tablets or capsules. On the basis of these studies, increased consumption of dietary vitamin A has been advocated (World Health Organization, 1984,1992). In India and Indonesia, the provision of extra vitamin A resulted in considerable reduction of mortality (ca. 40%) in preschool children (Bhandari et al 1994 Humphrey et al, 1996). While the efficacy of excessive oral doses over more than 8-12 weeks has been questioned, it is evident that an insufficient, low dose given once per week is apparently of little effect on morbidity or mortality (Ramakrishnan et al, 1995a,b). Indeed, recurrent diarrheal episodes or the existence of malnutrition may explain the poor efficacy seen with oral supplementation with low doses (Ramakrishnan et al., 1995a). 

If a botanical is shown to reverse an abnormal test result, modify another drug s adverse event, or act synergistically with another modality, it will usually be best developed as a drug. This is especially true if the botanical provides a distinct benefit for a patient population, but would pose safety concerns if used by the general public. In contrast to prevention, risk-reduction, or health-maintenance trials, therapeutic studies are often able to demonstrate clinical benefit with smaller numbers of subjects and with more tangible measures of outcome. 

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