Rule of reciprocity

This observation illustrates the so-called rule of reciprocity a body radiates strongly at those frequencies that it is able to absorb, and emits weakly at other frequencies. 

From the definition (9) it follows that theoretically both parameters G and U are equivalent, as might be expected for the probabilities of two contrary events (substance — void). Since the values G and U are mutually complementary to unity, it is possible to formulate for porous systems a rule of reciprocals If there is a porous system where the volume of voids is and the volume of solid matter V, an exchange of these parameters (V becoming V ) would yield a new porous... 

Eq. (12) has commonly been used, e.g. in the analysis of mass and gas transfer in gas-filled systems. From this relationship it may be deduced that varies from 0 to 00 and that = 1 when G = 0.5. Systems for which G 4 0.5 are poorly gas-filled ( low-porous ) and those with G > 0.5 are highly gas-filled . The rule of reciprocals ( reversal rule ) facilitates the analysis of gas-filled structures such as foamed plastics by enabling the use of the so-called complementary gas-filled (porous, cellular) systems. The complementary systems relate to each other as a mold and casting or negative and positive . 

Because of the reciprocating action of the piston, care must be exer-ci.sed to size the piping to minimize acoustical pulsations and mechanical vibrations. As a rule of thumb, suction and discharge lines should be sized for a maximum actual velocity of 30 ft/.sec (1,800 ft/min) to 42 ft/sec (2,500 ft/min). Volume 1 contains the necessary formulas for determining pressure drop and velocity in gas piping. 

Natural mutation of amino acids in the core of a protein can stabilize the same fold with different complementary amino acid types, but they can also cause a different fold of that particular portion. If the sequence identity is lower than 30% it is much more difficult to identify a homologous structure. Other strategies like secondary structure predictions combined with knowledge-based rules about reciprocal exchange of residues are necessary. If there is a reliable assumption for common fold then it is possible to identify intra- and intermolecular interacting residues by search for correlated complementary mutations of residues by correlated mutation analysis, CMA (see e.g., http //www.fmp-berlin.de/SSFA). 

Words that can be used as topics in essays 5% rale buffer common ion effect equilibrium expression equivalence point Henderson-Hasselbalch equation heterogeneous equilibria homogeneous equilibria indicator ion product, P Ka Kb Kc Keq KP Ksp Kw law of mass action Le Chatelier s principle limiting reactant method of successive approximation net ionic equation percent dissociation pH P Ka P Kb pOH reaction quotient, Q reciprocal rule rule of multiple equilibria solubility spectator ions strong acid strong base van t Hoff equation weak acid weak base... 

Modifying the rules of adding reciprocals of energy characteristics of subsystems as applied to complex structures we can obtain [6] the equation for calculating Pc-parameters of complex structure ... 

Next, consider the set of all real numbers except zero, and let the rule of combination be ordinary multiplication. The product of two nonzero real numbers is a nonzero real number, so that closure is satisfied. Associativity is satisfied. The identity element is 1. Finally, every element has an inverse, the inverse being the ordinary arithmetical reciprocal of the number. The set of all nonzero real numbers forms a group under ordinary multiplication. This group is of infinite order. (If zero were included in the set, we would not have a group, since zero would have no inverse.)... 

Compression Ratio. In order to save on equipment cost, it is desirable to use as few stages of compression as possible. As a rule, the compression ratio is limited by a practical desirability to keep outlet temperatures below 300°F or so to minimize the possibility of ignition of machine lubricants, as well as the effect that power requirement goes up as outlet temperature goes up. Typical compression ratios of reciprocating equipment are ... 

There are special rules for the sum and difference of reciprocals. Memorizing this formula might help you be more efficient when taking the GRE test ... 

The result obtained makes it possible to decide whether it is necessary to take account of a variation of the volume of any liquid due to the dissolution of a solid substance or it can be neglected in comparison with other possible errors. To do this, one must know an experimenal value of the density of the saturated solution. If not available, it may readily be estimated using the rule of additivity of the reciprocals 1/psoiution = l/pr + 1/p. ... 

There is plenty of experience with small reciprocating compressors for this service. Therefore, we have a pretty good understanding of the cost of these machines. The common rule of thumb for the cost of a reciprocating compressor is 1000 per hp for carbon steel construction. This can be multiplied by a material factor of between 3 and 4 to account for the use of 316L stainless steel. A larger factor is required if more exotic material is specified. 

This rule of thumb translates into n = 1 in equation (12.1). Furthermore, from my personal files, table 12.1 presents the cost of a small reciprocating compressor. Substituting this into equation... 

Ostwald, recalculated so as to give the equivalent conductances in ohm cm. units, instead of reciprocal Siemens units they show that the equation given above is approximately true, and hence it may be employed to determine the basicity of an acid. The method fails when applied to very weak acids whose salts are considerably hydrolyzed in solution. The results quoted in Table XX are perhaps exceptionally favorable, for the agreement with equation (27) is not always as good as these figures would imply. The Ostwald rule is, nevertheless, an expression of the facts already discussed, viz., that substances of the same valence type have approximately the same conductance ratios at equivalent concentrations and that the values diminish with increasing valence of one or both ions. The rule has been extended by Bredig (1894) to include electrolytes of various types. 

Fig. 19.8 relates motor horse power to cubic yards of concrete for both reciprocal and centrifugal compressors. It is based on the rule of thumb that foundation weight should be 5 times the compressor weight. 

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