Avoid Complexities

1 On Array Gain Some readers may by now have noticed that very little attention has been given to the gain of the array. This should not be interpreted as lack of interest in that subject. Rather it reflects the fact that it can be obtained in a forward and simple manner. 

It was already pointed out in Chapter 2, Section 2.6.2, that a large array with groundplane, uniform illumination, and physical area A also has a receiving area equal to A. Thus, if the array is designed to have no grating lobes and no significant surface waves, we may conclude from one of the most fundamental laws in antenna theory that the directivity D of the array is 

If the aperture illumination is tapered, the directivity in (6.2) should be multiplied by the aperture efficiency. That depends only on the aperture distribution [104]. 

Finally, the gain G is obtained from (6.2) by multiplication of the loss efficiency. Most commonly we are here talking about transmission line loss in the feeding harness and possibly some from the dielectric substrate supporting the elements. 

we must add the mismatch loss. If the antenna has a VSWR 2 (as typical for the arrays discussed here), the mismatch loss will be less than 0.5 dB. 

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As with safety, environmental considerations are usually left to a late stage in the design. However, like safety, early decisions often can lead to difficult environmental problems which later require complex solutions. Again, it is better to consider effluent problems as the design progresses in order to avoid complex waste treatment systems. 

These can be prepared by electrolytic oxidation of chlorates(V) or by neutralisation of the acid with metals. Many chlorates(VII) are very soluble in water and indeed barium and magnesium chlorates-(VII) form hydrates of such low vapour pressure that they can be used as desiccants. The chlorate(VII) ion shows the least tendency of any negative ion to behave as a ligand, i.e. to form complexes with cations, and hence solutions of chlorates (VII) are used when it is desired to avoid complex formation in solution. 

Avoid complex sentences containing more than one negative. 

Treatment chemicals should preferably be fed to the FW tank to minimize sludge deposits in the coils. Hydroxide alkalinity in ppm (mg/1) CaC03 must be maintained at a sufficient concentration to keep silica soluble and avoid complex silicate deposits. These precautions are necessary because scale-control internal treatment chemicals usually are not employed to assist in the prevention of such deposits in coil-type steam generators. 

Constraints might be applied for the sake of reducing the capital costs (e.g. to avoid long pipe runs). In addition, constraints might be applied to avoid complex heat integration arrangements for the sake of operability and control (e.g. to have heat recovery to a reboiler from a single source of heat, rather than two or three sources of heat). 

Because of the nature of PCR the identifications can be made either directly from clinical or environmental samples or after culture. However, because environmental samples contain many bacterial species, among which bacilli are the most common, the design of primers is important to avoid complex mixtures of PCR products. Such mixtures are extremely difficult to analyze by direct MS analysis. Furthermore the sensitivity of the analysis may be compromised if the signal is spread among many components. Successful analysis directly from environmental samples therefore is still a topic for current research. 

Rhodium complexes catalyze hydrosilylation-cyclization of 1,6-allenynes in the presence of (MeO SiH.77 To avoid complex product distributions, the use of substrates possessing fully substituted alkyne and allene termini is imperative. As shown in the cyclization of 1,6-allenyne 62a, the regiochemistry of silane incorporation differs from that observed in the rhodium-catalyzed hydrosilylation-cyclization of 1,6-enynes (see Section 10.10.2.3.2). For allenyne substrates, allene silylation occurs in preference to alkyne silylation (Scheme 40). 

Using Simple Methods That Avoid Complex Assumptions... 

The coupling of SR with POX is termed autothermal reforming (ATR). The exact definition varies. Some define ATR as an SR reaction and a POX reaction that take place over microscopic distances at the same catalytic site thus avoiding complex heat exchanging (16). Others have the less restrictive definition that ATR occurs when there is no wall between a combined SR reaction and catalytic POX reaction. ATR is carried out in the presence of a catalyst that controls the reaction pathways and thereby determines the relative extents of the POX and SR reactions. The SR reaction absorbs part of the heat generated by the POX process reaction, limiting the maximum temperature in the reactor. The net result is a slightly exothermic process. 

The theme of this book is the formation, transformation, and application of ion-radicals in typical conditions of organic synthesis. Avoiding complex mathematics, this book presents an overview of organic ion-radical reactions and explains the principles of the ion-radical organic chemistry. Methods of determining ion-radical mechanisms and controlling ion-radical reactions are also... 

Bullet points are a handy method for avoiding complex sentence structure and are also convenient for the final user of the document, e.g.,... 

Interestingly, too much security can have the undesired effect of reducing protection. If controls are too rigid, making normal productivity difficult, workers have a tendency to develop techniques for circumventing security measures. Complex electronic key doors are wedged open. Passwords are recorded on desk calendars. Systems are not turned off when unattended to avoid complex log-in procedures. In developing security controls a balance with appropriate access must be considered. 

Consider a single-component real process Y(t) in some fixed interval 0 < t < T. Each realization Yx(t) is an ordinary function of t and may be Fourier-transformed in this interval. To avoid complex coefficients we use the sine transform... 

With only a single site available for substitution, the Pd11 complex of tridentate diethylenetriamine, [(dien)Pd(H20)]2+, avoids complexities associated with a chelating metal ion and provides a facile intrinsic measure of binding at individual nucleic-base sites. Titration yields an endpoint after... 

The library synthetic steps were carefully adjusted to avoid complex purification procedures, but even the simple washing/drying/extraction... 

In order to properly formulate physical principles, some mathematics is indispensable and we cannot always avoid complex and abstract formalisms. To that end, specialized techniques that are sometimes particularly suited in solving certain types of problems will be Introduced when needed, mostly in the appendices to Volume 1. However, the reader is assumed to be familiar with elementary calculus. 

Avoid complex therapeutic regimens where possible The number of medications used should be kept to a minimum. In addition, the use of medications or dosage regimens that permit less frequent administration may help avoid interactions that result from an alteration of absorption (e.g., when a drug is administered in close proximity to meals). 

However, Table 2.3 does illustrate the need to take full account of the inherent complexity of the system, rather than seeking to reduce or avoid complexity altogether, when investigating organic farming. The challenge is to develop approaches that embrace as many of these interactions as possible. 

Keep requests and demands of the patient simple, and avoid complex tasks that might lead to frustration. 

Figure 19.5. In the course of developing the robotic platform ARCoSyn for fully automated synthesis and purification of compound arrays, a sample-oriented concept has been realized that subordinates sample functionality, thus avoiding complex transport processes between spatially separated individual functionalities. The central component is an industrial robot, which - in respect of flexibility (the gripper changing system for several centralized functions), work space (optimal utilization of available surface area, no need for a translation axis), precision, and loading capacity (option of using modules for both miniaturization and upscaling) - is adapted to the requirements of the laboratory automation concept.

To avoid complexity, we will limit the fast variable evaluation of F[5 x(r)] to times t that are short relative to the fluid s motional response times T. (An outline description of fast particle motion for times r > t is given in Section IV.A and Figure 3.5.)... 

Replacing (Fo xH)jc in ts by the virtual electric field JEjs and choosing the space fixed coordinate system so that its unit vector Cy points in the direction of Etl in order to avoid complex numbers in the subsequent numerical treatment, the nonvanishing matrix elements of which are diagonal in the rotational quantum numbers J and K are ... 

The library synthetic steps were carefully adjusted to avoid complex purification procedures, but even the simple washing/drying/extraction procedures made this library synthesis rather laborious and time requiring. The authors, in fact, synthesised only 600 discrete compounds of the 3078 which were planned in the library design. This either calls for simpler and effective work-up procedures for multistep solution libraries, which are very difficult to identify, or new automated techniques to overcome the purification/work-up bottleneck (see some of the following paragraphs). 

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