Family of systems

Alcohol (18) is used in the manufacture of demeton, a family of systemic insecticides. How can it be Tade ... 

If we consider one-parametric families of systems, then appearance of systems with two comparable constants may be unavoidable. Let us imagine a continuous path fc,(s) (s e [0,1], s is a parameter along the path) in the space of systems, which goes from one system with well-separated constants (s = 0) to another such system (s = 1). On this path fc,(s) such a point s that fc,(s) = fcy(s) may exist, and this existence may be stable, that is, such a point persists under continuous perturbations. This means that on a path there may be points where not all the constants are well separated, and trajectories of some constants may intersect. 

In N-parametric families of systems N+1 smallest constants can meet, and near such a "meeting point" a slow auxiliary cycle of N+1 reactions determines behavior of the entire cycle. 

The connective tissue disorders comprise a unique family of systemic diseases that have distinctive yet nonspecific systemic manifestations associated with organ involvement. Such diseases as rheumatoid arthritis (RA), rheumatic fever, systemic lupus erythematosus (SEE), scleroderma, and periarteritis nodosa all demonstrate the typical histologic and clinical findings characteristic of this category of diseases. 

If we now turn to the second family of systems under discussion, namely that involving halogens as cocatalysts, and principally chlorine, we find again that the evidence in favour of initiation by halonium ions such as Cl produced in the interaction with the catalyst is not entirely satisfactory. Indeed, the arguments based on the formation of certain chlorinated products in studies conducted with the model compound 2,4,4-tri-methylpentene-1 are not conclusive, since the same results, in lower yields, were... 

Barton and co-workers have developed a family of systems for oxidation and oxidative functionalization of alkanes under mild conditions exhibiting unusual selectivity (see reviews [50], polemics [50d,e], the first publication [51] and some recent publications[52], as well as the papers of other authors concerning these systems[53]). These oxidations occur in pyridine in the presence of an organic acid and are catalyzed by complexes of transition metals (mainly iron). If dioxygen is used as an oxidizing regent, a reductant must also take part in the reaction. The first such a system was invented in Gif-sur-Yvette [51]. Thus their name Gif systems. The systems with geographically based names are mentioned in Table IX.5. All Gif systems have the same chemical peculiarities ... 

The original MTM system is now known as MTM-1. Subsequent modifications were later developed to provide easier and quicker systems by condensing emd reducing the number of motion options and time values. MTM-2 and MTM-3 are exeunples of second-level and third-level MTM data. In addition, the MTM family of systems include MTM-V, MTM-C, MTM-M, MTM-TE, MTM-MEK, and MTM-UAS. 

Note this is the scheme commonly used for many personal computer operating systems, including the Windows family of systems.)... 

Following Meakin and Ernst (1988), we assume that the transient period well before the attainment of steady state is aggregation dominated. Suppose we now allow the breakage parameter k to vary (continuously) from one system to another among a (continuous) collection of systems characterized by k. (The system in which no breakage occurs belongs to this family of systems with k = 0.) Then we shall be concerned with the number density / (x, t k) of particles of size x at instant t in system /c, which satisfies the population balance given by... 

The details of which instrument is displayed in which position should not be fixed in the software but should be easy to change. This will allow a family of systems to use the same software and also provide for a limited amount of installation-time or in-flight customisation (e.g. a choice of presentation, or a choice between two different instruments that convey the same information). 

The aim of our development is to derive a detailed yet generic specification of resilient SoS. The resulting generic Event-B development can be applied (by formal instantiation) to a family of systems sharing similar traits. We cover a class of SoS that have the following characteristics ... 

In 2011, the Chinese Academy of Sciences launched a project to develop ADS and LFR technology, and the CLEAR family of systems was selected as the reference for both the ADS and the LFR. CLEAR consists of three stages a 10 MW, lead-based research reactor (CLEAR-I), a 100 MW lead-based engineering demonstration reactor (CLEAR-II), and a 1000 MW lead-based commercial prototype reactor (CLEAR-III) (Wu et al., 2013). 

I will be focusing specifically on ways in which both existing systems can be harnessed to greater benefit and on new product developments and enhancements. For many years the contractual relationship of maintainer and owner has existed particularly within the Rail Vehicle Engineering area. That relationship has for many years been supported by a family of systems colloquially known as RAVERS which have provided the vehicle owner with maintenance history and future planning records and to a lesser degree facilitated the planning of the work of the maintainer. 

Therefore, to study the transition from D to Z>, it is sufficient to examine a one-parameter family of systems such that XyxQ G D. Furthermore, since all qualitative changes in the phase portrait must occur in a small neighborhood of some non-rough special trajectory, we can restrict our consideration to the given neighborhood. 

Bifurcations in finite-parameter families of systems. Andronov s setup... 

In principle, to solve a bifurcation problem we need to consider all systems close to XsQ, This means that we must consider the Banach space of all small perturbations." On the other hand, when it is possible to reduce the analysis to some appropriate finite-parameter family of systems, the study is simplified significantly. 

In general, when dealing with a p-parameter family of systems we assume the following natural restrictions ... 

Consider a family of systems of differential equations which is C -smooth (r > 3) with respect to the variables x R, y G R (m > 0) and parameters e MP p > 1). Let the system have, at = 0, an equilibrium state O with a pair of purely imaginary characteristic exponents the rest are assumed to lie to the left of the imaginary axis. Since the equilibrium state has no zero eigenvalues, it persists in a small neighborhood of s = 0. Without loss of generality we may suppose that it resides at the origin for all small e. Let us assume that this is a pair of characteristic exponents closest to the imaginary axis... 

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