Dangerous boundaries

Some plausible safety issues of SVO have been revealed by our approach - it is dangerous to let low speed UAV avoid high speed UAV in some situations the 45 encounter angle for crossing is a dangerous boundary value for SVO the SVO algorithm is sensitive to sensor noise on velocity. 

Safe boundaries are such that crossing over them leads to only small quantitative changes of the system s state. Dangerous boundaries are such that arbitrarily small perturbations of the system beyond them cause significant and irreversible changes in the system s behavior. 

The latter comment is only heuristic. It reflects the influence of small noise, which always persists in real systems (moreover, it is well-known that fluctuations near bifurcational thresholds are amplified). Therefore, a representative point may break loose from an old regime even before the system reaches the dangerous boundary. 

Both cases have much in common in the sense that the imstable set of both bifurcating equilibrium states is one-dimensional. If the unstable set of the critical equilibrimn state is of a higher-dimension, then the subsequent picture may be completely different. Figure 14.3.1 depicts such a situation. When the imstable cycle shrinks into the equilibrium state we have a dilemma the representative point may jump either to the stable node 0 or to the stable node 02- Therefore this dangerous boundary must be classified as dynamically indefinite. 

Bautin, N. N. and Shilnikov, L. P. [1980] Suplement I Safe and dangerous boundaries of stability regions, The Hopf Bifurcation and Its Applications Russian translation of the book by Marsden, J. E. and McCracken, M. (Mir Moscow). 

Condensation will appear on the inside surface of porous or impervious materials, forming first on the worst insulated surfaces (normally glazing or steelwork). On porous surfaces condensation can occur within the material or at an internal boundary. This is known as interstitial condensation, and it is especially dangerous, since it is often not known about until it has caused noticeable damage. Condensation can be avoided or reduced by several methods ... 

Solders are cathodic to steel, zinc and cadmium, and anodic to Monel metal. Although tin or tin-coated metals may be used safely in contact with aluminium when they are not fused with it, a joint in aluminium made with a tin-lead solder is liable to destructive corrosion. The formation, on fusion, of the grain-boundary state, which, as already mentioned, makes aluminium so dangerous an impurity in tin, is responsible. Tin-zinc solders may be used the zinc gives a useful degree of protection. 

During many decades a factory has spilled polychlorinated biphenyls (PCBs) into a small creek which leads to a small lake. Meanwhile the pollution has stopped, yet the local authorities are afraid that PCB concentrations in the outlet of the lake may still be dangerous for the drinking-water supply operating on the aquifer further downstream. You are asked to make a first guess whether this fear may be substantiated. You decide to use a simple box model. Where would you draw the boundaries of the model and which subcompartments (if any) would you choose ... 

This task is carried out by means of a special aluminium or aluminium tipped steel fork. Local overheating followed by decomposition of the nitrocellulose can occur at the boundary of the add-wet and dry substance, if immersion is not uniform. This danger is particularly liable to occur with insufficiently purified cellulose, which does not readily take up the mixed add. 

Every model has limitations. Even the most robust and best-validated regression model will not predict the outcome for all catalysts. Therefore, you must define the application domain of the model. Usually, interpolation within the model space will yield acceptable results. Extrapolation is more dangerous, and should be done only in cases where the new catalysts or reaction conditions are sufficiently close to the model. There are several statistical parameters for measuring this closeness, such as the distance to the nearest neighbor within the model space (see the discussion on catalyst diversity in Section 6.3.5). Another approach uses the effective prediction domain (EPD), which defines the prediction boundaries of regression models with correlated variables [105]. 

During the prosecution period it is possible to refine the main claims of the application. It is not possible to materially change or extend them beyond the original boundaries. If it is found that the original claims are insufficient to do justice to the invention, it is possible to abandon and resubmit a new application. This new filing will, of course, have a later priority date. This action will increase the danger of being beaten by the competition, if they have filed an application between the two dates. 

Which method to use. Section 8.2.8 draws attention to the systematic nature of the limitations of packed-tower pressure drop correlations. Due to this systematic nature, the author warns against basing packing pressure drop calculations on any correlations whose limitations are not well known. Section 8.2.8 presents three correlations and elaborates on their limitations and application boundaries. Within their boundaries, these correlations should give reliable predictions. UBe of any other correlation is dangerous unless its limitations are explored. 

With the equations of secs. 4.6a-c the problem of computing f from mobilities at given Ka is in principle soluble. But not in practice The mathematics are very complicated and require a number of finesses, whereas simplifications is dangerous because the various fluxes and forces are coupled, so that approximating only one of these may offset the balance and misrepresent characteristic features. Moreover, the boundary conditions are in part determined by the composition of, and the mobilities of ions in the various parts of the double layer, for which model assumptions must be made. 

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