Numerical identity

During emulsification new surfaces are created between the two phases. Such a process requires energy the surface free energy, numerically identical to the easily measured surface tension, reflects this amount. 

The pAT values of a wide variety of organic compounds have been determined in DMSO. Some of these values are included in Table 7.2. It is not expected that the values will be numerically identical with aqueous pAT values, but for most compounds the same relative order of acidify is observed for hydrocarbons of similar structural type. 

Thus, the charge of an electron is equal but opposite to that carried by a hydrogen ion. The calculated result of the quantity of electricity carried by a single ion shows that where the gram-ionic weight of an ion is numerically identical with the gram-equivalent, that is when the ion is univalent, the ion carries a charge equal to that of an electron. It can be... 

The standard states are selected as m = 1 mol kg-1 and = 1 mol dm-3. In this convention, the ratio m./m is numerically identical with the actual molality (expressed in units of moles per kilogram). This is, however, the... 

The word "polymer" (first proposed by Berzelius in 1833) is made of "poly" from the ancient Greek word "mlvq" meaning "many" and "pepot " meaning "part". Polymers are molecules built up from numerous identical chemical "units" spatially repeated to form a chain. From the early times and still nowadays, a distinction is often made between "natural" and "synthetic" polymers, but it is somewhat artificial as natural polymers can now sometimes be synthesized (e.g., synthetic "natural rubber") and some synthetic polymers, which are never found in nature, can be synthesized by natural ways (enzymatic syntheses). 

The curve is symmetrical around the mean, which is numerically identical to the median and mode. The SD should be indicated 1SD lies approximately one third of the way between X and the end of the curve. 

Figure 7.4 plots the value of either of the off-diagonal elements (they are theoretically and numerically identical) of the (Af AO" matrix as a function of the location of the second experiment. As stated previously, the off-diagonal elements of the X Xy matrix are associated with the covariance of the parameter estimates for this model, the off-diagonals of the matrix represent the covariance between and... 

A dilute emulsion comprising oil drops dispersed in an aqueous solution was sheared between two glass slides under an optical microscope [149]. Original drops were deformed into long threads (Fig. 1.13a) that broke in numerous identical aligned and regularly spaced droplets (Fig. 1.13b). One can distinguish some very... 

This is formally but not numerically identical to the factor in Eq. (22). Therefore, a comparison of the Kyot-values from Eqs. (22) and (24) does not yield more than a qualitative check on the relative complex formation constants in the membrane solvent ... 

The ALIs and DACs recommended by the EPA are numerically identical to those recommended by the ICRP Publication 30 (ICRP 1979)... 

Solution The density of air is insignificant compared to the liquid hence p can be used for Ap. Because the density is given in cgs units, it is convenient to use this system of units throughout remember, millijoule meter 2 and erg cm 2 are numerically identical. Substituting numerical values into Equation (74) gives... 

Wiesner and coworkers have emphasized that while the equilibrium constants between the two diastereomeric photoexcited states and anionic intermediates respectively should be similar, there is no reason to expect that they must be numerically identical. Small differences in equilibrium constants could in some cases reverse the stereoselectivity of photocycloaddition with respect to metal reduction. The group of Cargill94 examined the validity of Wiesner s models by the photoaddition of tert-butylcyclohexenone 178 with ethylene. Irradiation at low temperature (—78 °C) afforded a mixture of three isomers 179-181, in which the photoproduct 179 is the major product while isomer 180, expected to be the major one based on the first model, was obtained as the minor isomer. This result seems to rule out the first model (it does not take into consideration the reversibility of the first bond formation in the intermolecular photoadditions), however, it is consistent with the second model (Scheme 39). 

In this case a full formal correspondence and numerical identity between polyelectronic equation (3) and orbital transcription equation (5) of vibronic... 

Aristotle s linking of numerical oneness with the having of unified matter, however, though it satisfies a common sense intuition about numerical identity, would seem to restrict the sort of entities that can be numbered to those entities that have matter. But, Aristode dearly thinks that there are entities that can be numbered that do not in any obvious way have. Motions, for instance, as Aristode s definition of time makes clear, can be numbered.6 So too can tones (Meta. 1016b24), categories, and unmoved movers (Meta. 1074al5). So it would seem that a fundamental tension exists in Aristode s account of number. 

The tension can be eased, however, if not ultimately removed, in a way consonant with Aristode s general philosophical tendencies. One might suppose that there is a fundamental sense of numerical identity that attaches to material substances, which can then be extended in... 

The angle between two sets of planes in any type of direct-space lattice is equal to the angle between the corresponding reciprocal-space lattice vectors, which are the plane normals. In the cubic system, the [h k /] direction is always perpendicular to the (h k 1) plane with numerically identical indices. For a cubic direct-space lattice, therefore, one merely substimtes the [h k 1] values for [u v w] in Eq. 10.57 to determine the angle between crystal planes with Miller indices h k l ) and (h2 h)- With all other lattice types, this simple... 

Note that the absolute weight change (in grams) is numerically identical to the weight percent change in a 100 g sample. 

Usually we use calories per gram per Kelvin, or BTU per pound per degree Rankine as units of heat capacity. Numerically, the two groups of units are identical. We also use heat capacity on a molar basis, in which case the units are per gram mole or per pound mole, and again these are numerically identical. 

PKa a logarithm of acid ionization constant (Ka) pKg Equivalent to -logioKe. where by convention Kg is the equilibrium dissociation constant of an antagonist. Numerically, identical to pAz for simple equilibrium competition at a single site, The term apparent pKe may be used when there is no evidence whether or not there is competition, but there is assumed to be (e.g. when calculating pKe from a single concentration of antagonist). PKC protein kinase C. 

Suppose 0.400 mole of SO2 and 0.200 mole of O2 are injected into a closed 1.00-liter container. When equilibrium is established (at time t, mole of SO3 has formed and that 0.344 mole of SO2 and 0.172 mole of O2 acted. The reaction does not go to completion. These changes are summarized in the following reaction summary, using molarity units rather than moles. (They are numerically identical here because the volume of the reaction vessel is 1.00 liter.) The net reaction is represented by the changes in concentrations. 

This book explores the coming of age of the discipline of the history of science - or more particularly, the history of chemistry - and the numerous identity problems associated with that tumultuous process. It avoids the perils of analytical irrelevance, and anchors abstract historiographical reflection to the concrete practices of historians, by approaching a set of interpretive issues and problems... 

Even though Eqs. (135) and (137) have a different structure they give numerically identical results. This follows from the permutation symmetry of the response function. In this case there is no computational advantage to use one expression before the other, we have to solve the same set of response equations in both cases. 

In this manner cultures consisting of numerous identical mycelium particles are obtained they have a diameter of about 5 mm. and have a globular, compact core of about 1 mm. diameter of pseudo-parenchymatic tissue. This core has appendices of about 2 mm length, arranged in a star shape, consisting of parallel hyphae. On completion of the cultivation after about 10 days, the mycelium is dark brown and the filtrate is an intense reddish brown color. The pH changes only insignificantly. 

The relationship between steady-shear viscosity and dynamic-shear viscosity is also a common fundamental rheological relationship to be examined. The Cox-Merz empirical rule (Cox, 1958) showed for most materials that the steady-shear-viscosity-shear-rate relationship was numerically identical to the dynamic-viscosity-frequency profile, or r] y ) = r] m). Subsequently, modified Cox-Merz rules have been developed for more complex systems (Gleissle and Hochstein, 2003, Doraiswamy et al., 1991). For example Doriswamy et al. (1991) have shown that a modified Cox-Merz relationship holds for filled polymer systems for which r](y ) = t] (yco), where y is the strain amplitude in dynamic shear. 

That is, the osmotic pressure obeys the generalised gas law, which includes Boyle s Law, Gay-Lussac s, and the Avogadro Hypothesis It will be observed that the R is numerically identical with the R of the perfect gas equation That is, the osmotic pressure of a dilute solution is related to the molecular volume, or the inverse of this the molecular concentration quantitatively as the pressure of a perfect gas is related to the volume For substances in dilute solution R = i 985 calones per gram-mole It may be noted that in the particular case in which V - v the osmotic pressure is identical with the gas pressure... 

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