J function

I he function/(r) is usually dependent upon other well-defined functions. A simple example 1)1 j functional would be the area under a curve, which takes a function/(r) defining the curve between two points and returns a number (the area, in this case). In the case of ni l the function depends upon the electron density, which would make Q a functional of p(r) in the simplest case/(r) would be equivalent to the density (i.e./(r) = p(r)). If the function /(r) were to depend in some way upon the gradients (or higher derivatives) of p(r) then the functional is referred to as being non-local, or gradient-corrected. By lonlrast, a local functional would only have a simple dependence upon p(r). In DFT the eiK igy functional is written as a sum of two terms ... 

The J function is plotted in Fig. 16-28 and tables are available (e.g., Sherwood et al., Ma.ss Transfer, McGraw-Hill, New York, 1975). Ver-meulen et al. (gen. refs.) discuss several approximations of the J function. For large arguments it approaches... 

A signihcant problem in tire combination of solid electrolytes with oxide electrodes arises from the difference in thermal expansion coefficients of the materials, leading to rupture of tire electrode/electrolyte interface when the fuel cell is, inevitably, subject to temperature cycles. Insufficient experimental data are available for most of tire elecuolytes and the perovskites as a function of temperature and oxygen partial pressure, which determines the stoichiometty of the perovskites, to make a quantitative assessment at the present time, and mostly decisions must be made from direct experiment. However, Steele (loc. cit.) observes that tire electrode Lao.eSro.rCoo.aFeo.sOs-j functions well in combination widr a ceria-gadolinia electrolyte since botlr have closely similar thermal expansion coefficients. 

Pospisil, J. Functionalized Oligomers and Polymers as Stabilizers for Conventional Polymers. Vol. 101, pp. 65-168. 

By omitting time-dependent terms, as in the preceding paragraph, the liP ) function may be read as the sum of the unperturbed wavefunction ) and a term which is the product of this function by a linear combination of the electronic coordinates, i.e. the Kirkwood s j) function. Thus, the (r) dipolar factor ensures gauge-invariance. But the role of the dipolar factor g f) in this mixed method is essential on the following point its contribution in the a computation occurs in a complementary (and sometimes preponderant) way to that calculated only from the n) excited states, the number of which is unavoidably limited by the computation limits. But before discussing their number, we have to comment the description of these states. 

R2. Raben, N., Exelbert, R., Spiegel, R., Sherman, J. B Nakajima, H., Plotz, P., and Heinisch, J., Functional expression of human mutant phosphofructokinase in yeast Genetic defects in French Canadian and Swiss patients with phosphofructokinase deficiency. Am. J. Hum. Genet. 56, 131-141 (1995). 

Since, in general, lower permeability media exhibit higher capillary-pressure suction, we argue that it is more difficult to stabilize foam when the permeability is low. Indeed the concept of a critical capillary pressure for foam longevity can be translated into a critical permeability through use of the universal Leverett capillary-pressure J-function (.13) and, by way of example, the constant-charge model in Equation 2 for II ... 

Farouq Ali S.M. and Selby R.J. "Function, Characteristics of EOR Foam Behaviour Covered in Laboratory Investigations" Technology, Oil... 

The Leverett J-function is used in reservoir engineering (22) to relate the permeability k, porosity < >, and wetting characteristics to water saturation S... 

Hagenbuch, B., Stieger, B., Foguet, M., Lubbert, H., Meier, P. J., Functional expression cloning and characterization of the hepatocyte Na+/bile add cotransport system,... 

BARBER, R.D., DONOHUE, T.J., Function of a glutathione-dependent formaldehyde dehydrogenase in Rhodobacter sphaeroides formaldehyde oxidation and assimilation, Biochemistry, 1998, 37, 530-537. 

Frechet, J. M. J. Functional polymers and dendrimers reactivity, molecular architecture and interfacial energy , Science, 263,1710-1715 (1994). 

Proof First, it is possible to verify that the < )j-functions are solutions of the Lie derivative Lgj x) = 0 given by the following partial differential equation... 

The values of the effective permeabilities vary over orders of magnitude, and this corresponds to the different results of the models. Furthermore, as discussed in various papers,the effective permeability of Natarajan and Nguyen (curve e) varies significantly over a very small pressure range, although they state that their capillary-pressure equation mimics data well. With respect to the various equations, the models that use the Leverett J-function all have a similar shape except for that of Berning and Djilali (curve a), who used a linear variation in the permeability with respect to the saturation. The differences in the other curves are due mainly to different values of porosity and saturated permeability. As mentioned above, only the models of Weber and Newman (curve d) and Nam and Kaviany (curve f) have hydrophobic pores, which is why they increase for positive capillary pressures. For the case of Weber and Newman, the curve has a stepped shape due to the integration of both a hydrophilic and a hydrophobic pore-size distribution. 

Zhang Y, Fan Y, Sun C, Shen D, Li Y, Li J. Functionalized polydiacetylene-glycoUpid vesicles interacted with Escherichia coli under the Ti02 colloid. CoUoids Surf B Biointerfaces 2005 40 137-142. 

Diplock, A.T., Charleux, J.-L., Crozier-Willi, G., Bung, P., Kok, F.J., Rice-Evans, C.A., Rober-froid, M., Stahl, W., and Vina-Ribes, J., Functional food science and defence against reactive oxidative species, Br. J. Nutr., 80, S77, 1998. 

Song, J. H. and Sailor, M. J. Functionalization of nanocrystalline porous silicon surfaces with aryllithium reagents Formation of silicon-carbon bonds by cleavage of silicon-silicon bonds. Journal of the American Chemical Society 120, 2376 (1998). 

Fitzgerald, D. R. and Doren, D. J. Functionalization of diamond(lOO) by cycloaddition of butadiene First-principles theory. Journal of the American Chemical Society 122,12334 (2000). 

REM J FUNCTION VALUE, DERIVATIVES AND DEFINITE t 4484 REN t INTEGRAL OF A CUBIC SPLINE AT A GIVEN -POINT t 4484 REN lltltllllltmillltlllltllltltllllllltltlllllttltll 4488 REN INPUT ... 

Munch-Petersen, B. Knecht, W. Lenz, C. Sondergaard, L. Piskur, J. Functional expression of a multisubstrate deoxyribonucleoside kinase from Drosophila melanogaster and its C-terminal deletion mutants. J. Biol. Chem., 275, 6673-6679 (2000)... 

Substituted benzaldehydes have proved useful as acid-base indicators for reactions involving the addition of hydroxide ions n strongly alkaline aqueous media (19). It seemed logical to extend their use to solutions of sodium hydroxide in water-ethanol and water-DMSO mixtures. In ethanol-water, it was of interest whether the competition between addition of hydroxide and ethoxide ions will be reflected in the dependence of the J- function on ethanol concentration. In water-DMSO mixtures, it was important to investigate whether the radical change at higher DMSO concentrations, observed for H values and attributed to changes in solvation of the hydroxide ion, will be observed for the addition reaction as well. 

---