Sensitivity state

As can be seen most of the tubes were still in a non-sensitive state while about ten were in runaway conditions. This wiU give an operational feel for how uniform the catalyst charge should be and how closely the system may approach incipient runaway, for a single tube in a multi-tube production unit. 

To scrutinize the sensitivity of the flame structure to the description of the outer-flow field, we compared the flame structure obtained from the two limiting boundary conditions at the extinction state, which can be considered to be the most aerodynamically and kinetically sensitive state of the flame for a given mixture concentration, and demonstrated that they were basically indistinguishable from each other. This result thus suggests that the reported discrepancies in the extinction stretch rates as mentioned in the work by Kee et al. [19] are simply the consequences of the "errors" associated with the evaluation of the velocity gradients. 

Lyon, R.A. Davis, K.A. and Titeler, M. H-DOB (4-bromo-2,5-emethoxy-phenylisopropylamine) labels a guanine nucleotide-sensitive state of cortical 5-HT2 receptors. J Pharmacol Exp Ther 31 194-199, 1987. 

Sanden, T., Persson, G., Thyberg, P., Blom, H. and Widengren, J. (2007). Monitoring kinetics of highly environment sensitive states of fluorescent molecules by modulated excitation and time-averaged fluorescence intensity recording. Anal. Chem. 79, 3330-41. 

At this point we ought to hold our breath if 999 photons per 1000 are absorbed (with only one being transmitted), then the detector measuring the intensity of the transmitted light I needs to be exceptionally sensitive. Stated another way, an absorbance of A = 3 is unlikely to be particularly accurate. 

To Excite the Plate.—Place it on a dipper, and immerse it quickly and without hesitation in a vertical bath of acetonllrata of silver, made thus —Distilled water one ounce, nitrate of silver fifty grains, glacial acetic acid one drachm. Leave It in the bath for a couplo of minutes, then wash it well in clean watar, and lastly in distilled watar, and set it up to dry. When dry put it away in the platebox until ready for use in the camera. It may be preserved in a sensitive state for several days. Some persons add a few drops of a solution of iodide of potassium to a new nitrate-bath, and filter it on the following day, in order to saturate it with iodide of silver. When this is done a new bath is not so liable t attack the iodide of silver in the film. 

These results demonstrated that Egyptian patients that were not cured by the recommended doses of praziquantel-harboured worms that were demonstrably less responsive to the drug both in vivo and in vitro. This fact produced concern that these worms could result in a large population of schistosomes that would not be cured by praziquantel. However, further study of these worms found two issues that would limit the spread of these less responsive worms in the field. Firstly, some of the isolates reverted to a praziquantel-sensitive state with the removal of praziquantel pressure. Secondly, all of the isolates that did not revert to a praziquantel sensitivity suffered from decreased biological fitness. 

Transitions to burst discharges with synchronization of large brain areas seem to be accompanied with a loss of sensitivity. Reduced sensitivity to environmental stimuli, of course, is not a problem but even required at the obviously well coordinated transition to sleep. However, it can become a problem when this happens while the neurons and network should be in a sensitive state for appropriate reactions on environmental information. Transitions to bursts and associated synchronization of complete nuclei can tune the system into an oscillatory and very stable internal state which makes it practically insensitive to external stimuli, e.g. during... 

Genetic. The differences between many susceptible and resistant cultivars are the abilities of the latter to appropriately respond quantitatively in time and in space to infection, rather than qualitative differences in biochemical pathways. This type of genetic resistance may be considered a form of an endogenous constitutively sensitized state. Genetic sensitization of a cultivar requires both a source of appropriate germplasm and a method of effective transfer and incorporation of the genetic material into the recipient cultivar. Both requirements cannot always be met. Furthermore, undesirable traits often accompany desired resistance traits. This very important area of plant sensitization, broadly construed, lies beyond the scope of this paper. 

With all of its variables identified, Eq. (3.6) provides a means to evaluate the effect of sample and instrument parameters on observed signal. An additional application of Eq. (3.6) is the comparison of different spectrometers for instrumental sensitivity. Stated differently, how much signal results from a particular sample for a given laser power and measurement time Rearrangement of Eq. (3.6) and (3.9) yields (3.10), which applies to the multichannel case (6) ... 

Because this class of functions has been used extensively to model cell growth kinetics, these functions can be modified to describe subpopulations of cells. The equations below describe a Gompertz growth model that has been modified to allow cells to oscillate between a therapeutically sensitive state (Rs) and a resistant state (Rr). The same modification can also be made to the simple growth model (28). 

The Ehrenfest classification is not too well suited for the description of real phase transitions occurring in nature. The above remark concerns most of all the phase transitions which are not first-order. Better suited for an examination and classification of phase transitions is the Landau classification. Landau s idea is based on an assumption that in the case of many phase transitions one may always find a quantity, called the parameter of order, whose small change (with respect to the value q — 0) causes a qualitative changes in the parameters of a body (this implies that for q = 0 the system is in the sensitive state). 

In chemical systems one may thus distinguish state variables and control parameters. Chemical reactions have been known from experience to be structurally stable (resistant to small changes in control parameters) under some conditions it is also known that the change in a reaction character (change in the stationary state or dynamics) may occur upon a continuous variation in control parameters in other words, the sensitive state may be created in a chemical system. The above remarks substantiate an attempt to apply catastrophe theory to a description of chemical reactions. 

The classification of sensitive states and the standard forms of dynamical systems describing a system in the vicinity of a specified sensitive state will be given. It is difficult to overestimate the efforts of mathematicians which have led them to classifying the standard forms of codimension one, two and (partly) three. Following the determination of the sensitive state of a given dynamical system, the nature of dynamics of catastrophes of this system may be inferred from knowledge of a suitable standard form. 

Classification of catastrophes will be preceded by the centre manifold theorem which is a counterpart to the splitting lemma in elementary catastrophe theory. It will turn out that in the catastrophe theory of dynamical systems such notions of elementary catastrophe theory as the catastrophe manifold, bifurcation set, sensitive state, splitting lemma, codimension, universal unfolding and structural stability are retained. 

When conditions (1)—(3) are not fulfilled, the Grobman-Hartman theorem is not valid. As will be shown later, then we have to deal with the sensitive state of a dynamical system (this corresponds to a degenerate critical point in elementary catastrophe theory). A generalization of the Grobman-Hartman theorem, the centre manifold theorem which may be regarded as a counterpart to the splitting lemma of elementary catastrophe theory, has been found to be very convenient in that case. 

Hence, let us characterize mo re exactly, in terms of eigenvalues of the stability matrix, the sensitive state appearing in such a case. 

Such a case is undoubtedly the sensitive state, since an arbitrarily small change in the control parameter ek may result in the appearance of a negative or positive /, value and in a qualitative change in the phase portrait, i.e. in a catastrophe. In other words, the case (5.25) divides qualitatively different states. 

The above observation may be employed for finding the remaining sensitive states of the system (5.2) on the basis of knowledge of its stability matrix a j and the classification of stationary states given in Section 5.1. The sensitive states are those corresponding to such values of the control parameters e that the eigenvalues of the stability matrix ay(e) are of the following form ... 

For A different from zero, the sensitive states (5.26) separate the following states... 

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