PFAFF 8320

If a Pfaff differential expression DF = Xdx + Tdy+Zdz has the property that every arbitrary neighbourhood of a point P(x, y, z) contains points that are inaccessible along a path corresponding to a solution of the equation DF = 0, then an integrating denominator exists. Physically this means that there are two mutually exclusive possibilities either a) a hierarchy of non-intersecting surfaces (x,y, z) = C, each with a different value of the constant C, represents the solutions DF = 0, in which case a point on one surface is inaccessible... 

D. Ganttei and D. Pfaff, eds., Neurohiology of Oxytocin, Spriagei-Vedag, Berha, 1986. 

Pfaff, m. rivet stamp nut driver Brewing) underlet. 

Strittmater, R., Watermeier, L and Pfaff, S., Symp. 9th, Cornell Univ., Ithaca, N.Y., 1962p. 311. Academic Press, New York, 1963. 

As we have seen earlier, the thermodynamic variables p, V, T, U, S, H, A, and G (that we will represent in the following discussion as W, X, T, and Z) are state functions. If one holds the number of moles and hence composition constant, the thermodynamic variables are related through two-dimensional Pfaffian equations. The differential for these functions in the Pfaff expression is an exact differential, since state functions form exact differentials. Thus, the relationships that we now give (and derive where necessary) apply to our thermodynamic variables. 

It can be shown mathematically that a two-dimensional Pfaffian equation (1.27) is either exact, or, if it is inexact, an integrating denominator can always be found to convert it into a new, exact, differential. (Such Pfaffians are said to be integrable.) When three or more independent variables are involved, however, a third possibility can occur the Pfaff differential can be inexact, but possesses no integrating denominator.x Caratheodory showed that expressions for SqKV appropriate to thermodynamic systems fall into the class of inexact but integrable differential expressions. That is, an integrating denominator exists that can convert the inexact differential into an exact differential. 

We have previously shown that the Pfaff differential <5pressure-volume work equation (2.43) is an inexact differential. It is easy to show that division of equation (2.43) by the absolute temperature T yields an exact differential expression. The division gives... 

Pfaff, T, Malitschek, B, Kaupmann, K, Prezeau, L, Pin, IP, Bettler, B and Karschin, A (1999) Alternative splicing generates a novel isoform of the rat metabotropic GABAgRl receptor. Eur. J. Neurosci. 11 2874-2882. 

Baier-Weber, B., Prox, A., Wachsmuth, H., and Breyer-Pfaff, ].,Drug Metab. Dispos., 16, 490 96, 1988. 

Fig. 4.6(b) GnRH +ve neurones (relative density) in the brain dot = mammalian, circle = avian, forms. Parasagittal view of distribution in Musk Shrew (Suncus murinus) — from bulb to median eminence (ME), optic X (OC), cerebral aqueduct (Aq), and preoptic area (POA) (from Schwanzel-Fukuda and Pfaff, 1994). 

Pfaff D.W., ed. (1985). Taste, Olfaction, and the Central Nervous System. Rockefeller University Press, New York, p. 346. 

Schwanzel-Fukuda M., Fadem B., Garcia M. and Pfaff D. (1988). Immunocytochemical localization of LHRH in the brain and Nervus terminalis of the adult and early neonatal Gray Short-Tailed opossum (Monodelphis domestica). J Comp Neurol 276, 44-60. 

Pfaff K (2012) Re-use of recycled materials in food contact applications in the perspective of consumer protection. Platform presentation (overheads) at the RiskCycle Conference risk-based management of chemicals and products in a circular economy at a global scale. 8-9 May 2012, Dresden, Germany (www.wadef.com/projects/riskcycle/)... 

Pfaff K, Hutzler C (2010) Gesundheitliche Bewertung der Ubergange von Mineralolen. Vortrag beim Workshop Mineralolanalytik im Lebensmittelbereich , Ziirich, 10/11 June 2010... 

McEwen, B. S., Jones, K. and Pfaff, D. Hormonal control of sexual behavior in the female rat molecular, cellular and neurochemical studies. Biol. Reprod. 36 37 15,1987. 

Pfaff, D. W. Estrogens and Brain Function, New York Springer-Verlag, 1980. 

Vasudevan N, Ogawa S, Pfaff D (2002) Estrogen and thyroid hormone receptor interactions physiological flexibility by molecular specificity. Physiol Rev 82 923... 

Lustig RH, Pfaff DW, Fishman J (1988) Opioidergic modulation of the oestradiol-induced LH surge in the rat roles of ovarian steroids. J Endocrinol 116 55-69... 

Scott RE, Wu-Peng XS, Pfaff DW (2002) Regulation and expression of progesterone receptor mRNA isoforms A and B in the male and female hypothalamus and pituitary following oestrogen treatment. J Neuroendocrinol 14 175-183... 

Shivers BD, Elarlan RE, Morrell JI, Pfaff DW (1983) Absence of oestradiol concentration in cell nuclei of LElREl-immunoreactive neurones. Nature 304 345-347... 

Pfaff, J.K., et al., Inhalation exposure to JP-8 jet fuel alters pulmonary function and substance P levels in Fischer 344 rats, J. Appl. Toxicol., 15, 249, 1995. 

Kavaliers, M., Choleris, E., Agmo, A. and Pfaff, D.W. (2004) Olfactory-mediated parasite recognition and avoidance linking genes to behavior. Horm. Behav. 46, 272-283. 

---