Differential system

Geometric Data Hematrack Automated Differential System Model-590, Operator s Manual, Geometric Data, Wayne, Pa., 1982. 

By autonomous we mean that F, Fit). This is not really a restriction since any non-autonomous system can always be transformed into an autonomous one by the addition of extra variables. Similarly, an N -order differential system can always be transformed to a first order one by introducing additional variables. 

Refractive index detectors. These bulk property detectors are based on the change of refractive index of the eluant from the column with respect to pure mobile phase. Although they are widely used, the refractive index detectors suffer from several disadvantages — lack of high sensitivity, lack of suitability for gradient elution, and the need for strict temperature control ( + 0.001 °C) to operate at their highest sensitivity. A pulseless pump, or a reciprocating pump equipped with a pulse dampener, must also be employed. The effect of these limitations may to some extent be overcome by the use of differential systems in which the column eluant is compared with a reference flow of pure mobile phase. The two chief types of RI detector are as follows. 

Z>) Variational Equations for Systems with n Variables.—It can be shown10 that for differential systems of the form... 

Consider a trajectory S of a differential system issuing for t = tQ from a point close to the origin. It is dear that 8 will never intersect a surface F = Fc from inside to outside as dVfdt is negative. 

Differential Systems.—For differential systems with constant coeffidents the following theorem holds ... 

We can now draw certain conclusions. Assume that we have a differential system... 

Edsberg, L., "Numerical Methods for Mass Action Kinetics" in Numerical Methods for Differential Systems, Lapidus, L. and Schlesser W.E., Eds., Academic Press, New York, NY, 1976. 

A different problem concerns the condensation of chromatin beyond the stage of nucleosomes into compact stacks. In these stacks the DNA is silent and it is known that the silencing depends on the presence of various DNA-binding proteins and their chemical modification. All of this complicated apparatus is part of the differentiation system but it is not known if any small molecules or ions are also involved (see Mohd-Sarip and Verrijzev in Further Reading). 

All heat evolutions which occur simultaneously, in a similar manner, in both twin calorimetric elements connected differentially, are evidently not recorded. This particularity of twin or differential systems is particularly useful to eliminate, at least partially, from the thermograms, secondary thermal phenomena which would otherwise complicate the analysis of the calorimetric data. The introduction of a dose of gas into a single adsorption cell, containing no adsorbent, appears, for instance, on the calorimetric record as a sharp peak because it is not possible to preheat the gas at the exact temperature of the calorimeter. However, when the dose of gas is introduced simultaneously in both adsorption cells, containing no adsorbent, the corresponding calorimetric curve is considerably reduced. Its area (0.5-3 mm2, at 200°C) is then much smaller than the area of most thermograms of adsorption ( 300 mm2), and no correction for the gas-temperature effect is usually needed (65). 

It is not surprising, therefore, that this dynamic technique was chosen to provide information on chiral interactions in compressed films. Given that these stereochemically differentiated systems may have dramatically different HI A isotherm characteristics, and hence different packing arrangements, it is plausible that their flow properties are stereochemically differentiated as well. 

Bogs, C., Battilani, P., and Geisen, R. (2006). Development of a molecular detection and differentiation system for ochratoxin A producing Penicillium species and its application to analyse the occurrence of Penicillium nordicum in cured meat. Int. J. Food Microbiol. 107, 39 7. 

We have not succeeded in integrating systems of ordinary differential systems 8.2 and 18 [Eq. (80)]. Furthermore, systems 19-21 coincide with system 5 and system 16 coincides with system 8.1. 

Hopf, E. (1942). Abzweigung einer periodischen Losung von einer stationaren Losung eines differential system. Ber. Math. Phys. Kl. Sachs. Acad. Wiss. Leipzig, 94, 1, 22. 

The subsequent ability of cells to induce triglyceride synthesis and storage is interfered with by incubation of growing (but not resting) cells with bromodeoxyuridine at 5/xM. This compound is known to interfere with several differentiating systems (Rutter et al., 1973) at concentrations which do not affect the rate of cell growth. 

This question has already been discussed in Sect. 2.6.2. It has been shown that two opposite situations may occur some simple mechanisms cannot be processed mathematically in a useful way, whereas some complex mechanisms can be solved explicitly to obtain rate laws. However, it is well known that, except for linear systems, there are no explicit solutions of differential systems. 

It is worth noting that some differential equations have been replaced by algebraic equations, which means that the order of the initial differential system has decreased and that the initial conditions on radical concentrations have been dropped. 

Equations for each of the perturbation functions xu yh Xu Yl are derived by substituting the asymptotic expansions into the initial differential system, by matching terms with the same power in e, and finally by writing the proper initial and boundary layer conditions. The zeroth-order outer approximation is the solution to the system... 

R.A. Willoughby (Ed.), Stiff Differential Systems, Plenum Press, New York, 1974. 

Kostoglou and Karabelas [93] solve the linear differential system (with the ttottlinear boundary conditions) for the case of one and two undulating... 

These are the well-known Orr-Sommerfeld equations for mixed convection flows, that show the disturbance normal velocity and the temperature fields to be coupled, constituting a sixth order differential system. Equations (6.4.10) and (6.4.11) are to be solved subject to the six boundary conditions ... 

BWh] L. P. Burton and W. M. Whyburn (1952), Minimax solutions of ordinary differential systems," Proceedings of the American Mathematical Society 3 794-803. 

---