Reciprocity relationship

In addition to the reciprocal relationship between the helix pitch and layer line spacing, Figure 18.14 illustrates the reciprocal relationship between the orientation of the arms of the cross and the angle of climb of the helix as the helix becomes steeper the arms of the cross become more horizontal. 

Under these conditions the reciprocal relationship fits the data extremely well, particularly at volume fractions below 0.5 of the strongly eluting solute. In addition, under these conditions the inverse will also apply, i.e.,... 

Scott and Beesley [2] measured the corrected retention volumes of the enantiomers of 4-benzyl-2-oxazolidinone employing hexane/ethanol mixtures as the mobile phase and correlated the corrected retention volume of each isomer to the reciprocal of the volume fraction of ethanol. The results they obtained at 25°C are shown in Figure 8. It is seen that the correlation is excellent and was equally so for four other temperatures that were examined. From the same experiments carried out at different absolute temperatures (T) and at different volume fractions of ethanol (c), the effect of temperature and mobile composition was identified using the equation for the free energy of distribution and the reciprocal relationship between the solvent composition and retention. 

Table 2.2 gives the pH scale. Note again the reciprocal relationship between [H ] and [OH ]. Also, because the pH scale is based on negative logarithms, low pH values represent the highest H concentrations (and the lowest OH concentrations, as K, specifies). Note also that... 

MFR tests are used to detect degradation in fabricated products where comparisons, as an example, are made of the MFR of pellets to the MFR of product. MFR has a reciprocal relationship to melt viscosity. This relationship of MW to MFR is an inverse one as the MFR increases, the MW drops. MW and melt viscosity is also related as one increases the other increases. 

Equation 9.126, known as the reciprocity relationship or reciprocal rule, then leads to the equation ... 

For a given geometry, view factors are related to each other, one example being the reciprocity relationship given in equation 9.126. Another important relationship is the summation rule which may be applied to the surfaces of a complete enclosure. In this case, all the radiation leaving one surface, say i, must arrive at all other surfaces in the enclosure so that, for n surfaces ... 

Substituting for Tr from this equation in equation 9.135 and noting, from the reciprocity relationship, that A2F2r = ArFr2, then ... 

Reciprocity relationship, radiation 448 Rectangular duct 87 Redman, J. 550, 566 Reduced coordinates 35... 

A Reciprocal Relationship Between Biochemistry Medicine Has Stimulated Mutual Advances... 

Chemokines serve as the messengers in a reciprocal relationship that exists between brain tumors and their environment (Fig. 11.1). Brain tumors are dependent upon stromal sources of chemokines for their growth and spread. They also use chemokines... 

The precise role of melatonin in sleep and waking is uncertain but it seems to act as a go-between for the light and biological cycles and evidence suggests that it has a reciprocal relationship with the SCN (Fig. 22.3). Its actions are mediated by (MLi) receptors which are found predominantly in the SCN as well as thalamic nuclei and the anterior pituitary. These are G protein-coupled receptors, with seven transmembrane domains, that inhibit adenylyl cyclase. Their activation by melatonin, or an MLi agonist such as 2-iodomelatonin, restores the impaired circadian cycle in aged rats. 

The method replaces a space of particular variables with a simplified space defined by axes. Variables, which, if they are correlated to each other, have a multiple piece of information that is difficult to identify, and are replaced with independent axes, which are supposed to have a piece of information decomposed into elementary elements. The arrangement of these variables in this new space enables establishment of their reciprocal relationships. 

Richman, A.L., Su, E.Y. and Ho, G. (1981). Reciprocal relationship of synovial fluid volume and oxygen tension. Arthritis Rheum. 24, 701-705. 

More than 99% of total body calcium is found in bone the remaining less than 1% is in the ECF and ICE Calcium plays a critical role in the transmission of nerve impulses, skeletal muscle contraction, myocardial contractions, maintenance of normal cellular permeability, and the formation of bones and teeth. There is a reciprocal relationship between the serum calcium concentration (normally 8.6 to 10.2 mg/dL [2.15 to 2.55 mmol/L]) and the serum phosphate concentration that is regulated by a complex interaction between parathyroid hormone, vitamin D, and calcitonin. About one-half of the serum calcium is bound to plasma proteins the other half is free ionized calcium. Given that the serum calcium has significant protein binding, the serum calcium concentration must be corrected in patients who have low albumin concentrations (the major serum protein). The most commonly used formula adds 0.8 mg/dL (0.2 mmol/L) of calcium for each gram of albumin deficiency as follows ... 

Dyson introduces a series of mathematical and physical simplifications and then reaches his important conclusions. These involve the reciprocal relationship of three parameters when these are chosen, the model is completely defined. The parameters are ... 

From the above discussion, it is obvious that response time of a system and its sensitivity are intrinsically linked. In fact they have a reciprocal relationship. As sensitivity increases it is possible to look at bimolecular reactions of species at lower and lower concentrations. In these circumstances the requirements on the response time for a system will get less and less. Of course, there are limits to how far this can be pushed, particularly with time resolved IR measurements in solutions, where absorption by the solvent is significant. Also, as indicated previously, coordination of a nascent photofragment by solvent molecules can occur on an exceedingly rapid timescale (15). Additionally, as the concentration of added reactant is diminished, reactions with impurities in the solvent or with small concentrations of atmospheric gases become a problem. Nevertheless, over a wide range of concentration there is a trade-off between minimum detectable signal and timescale. 

This reciprocal relationship is a general property of Fourier transforms. The -function of the previous paragraph and its transform demonstrate the same reciprocity. To characterise this property more precisely a bracket function, called a scalar or inner (dot) product, is used to define an overlap integral... 

The important result is the obvious symmetry between TM1/ and R u as shown in (42) and (43). Both of these tensors vanish in empty euclidean space and a reciprocal relationship between them is inferred The presence of matter causes space to curl up and curvature of space generates matter. 

Onsager s theorem consists of proving that a reciprocal relationship of the type Lap = Lpa between the affinities and fluxes of coupled irreversible processes is universally valid in the absence of magnetic fields. 

Onsager found a proof of the general reciprocal relationship by consideration of natural fluctuations that occur in equilibrium systems. It is argued that an imbalance like that which initially exists when two reservoirs are connected as in figure 2, could also arise because of natural fluctuations. When the occasional large fluctuation occurs in an equilibrium system, the subsequent decay of the imbalance would be indistinguishable from the decay that follows deliberate connection of the reservoirs. 

Figure A1.2 The electromagnetic spectrum, showing the reciprocal relationship between wavelength (in metres) and frequency (in Hertz, or cycles per second). The visible band is a very narrow region, with wavelengths between 400 and 700 nm. (Adapted from Physical Science Study Committee, 1960 Figure 31-27, reprinted by permission of D.C. Heath and Company.)...

Although humans differ greatly from insects, a reciprocal relationship between humans and plants... 

---