Partial mixing

The change in the order of differentiation to give the last term in equation A.29 is permissible because the velocity field will satisfy the sufficient conditions, namely that the two mixed partial derivatives are continuous. Equation A.27 can now be written as... 

Formula A complex mixture of polyoxyethylene ethers of mixed partial oleic esters of sorbitol anhydrides Density 1.06-1.llOgml-1 Volatility High... 

Ergotamine Mixed partial agonist effects at 5-HT2 and (X adrenoceptors Causes marked smooth muscle contraction but blocks cx-agonist vasoconstriction Migraine and cluster headache Oral, parenteral duration 12-24 h Toxicity Prolonged vasospasm causing gangrene uterine spasm... 

Ergonovine Mixed partial agonist effects at 5-HT2 and tx adrenoceptors Same as ergotamine some selectivity for uterine smooth muscle Postpartum bleeding migraine headache Oral, parenteral (methylergonovine) duration 2-4 h Toxicity Same as ergotamine... 

The Euler criterion is therefore equivalent to the familiar mixed partials of a function are equal rule of calculus. This cross-differentiation rule is also the condition for the function z(x, y) to have well-defined (single-valued) first derivatives at each point, and thus to be graphable. 

Moreover, from the first-law (Maxwell-type exactness) relationship between mixed partial derivatives, as expressed by (8.80), we see that the (R R/) values also satisfy the symmetric property (9.27b) ... 

The l.h.s. of Eq. (2.38) is the /th element of the vector g(4+I). On the r.h.s. of Eq. (2.38), since the partial derivative of q with respect to its / th coordinate is simply the unit vector in the /th coordinate direction, the various matrix multiplications simply produce the / th element of the multiplied vectors. Because mixed partial derivative values are independent of the order of differentiation, the Hessian matrix is Hermitian, and we may simplify Eq. (2.38) as... 

ALCOHOLYSIS. If a triglyceride oil is heated with a polyol, such as glycerol or pentaerythntol, mixed partial esters are produced rn a reaction known as alcoholysis. 

CA 55, 14918 (1961) [Comp proplnt prepd by filling a mold with previously mixed partially unsaturated polyester, NG (or DEGDN) and Amm perchlorate or picrate, etc and leaving the dough to harden] T)G.D.Sam-mons, USP 2969638 (1961) CA 55, 11850... 

VonVoigtlander PF, Lewis RA (1983) A withdrawal hyperalgesia test for physical dependence evaluation of p. and mixed-partial opioid agonists. J Pharm Meth 10 277-282 Way EL (1993) Opioid tolerance and physical dependence and their relationship. In Herz A, Akil H, Simon EJ (eds) Handbook of Experimental Pharmacology, Vol 104/ Opioids II, chapter 53. Springer Berlin Heidelberg New York, pp 573-596... 

By considering the combined variable z = x — xj2, we remove the mixed partial differential term from Eq. (4.293). The transformation obtained is the hyperbolic partial differential equation (4.294). This equation represents a new form of the stochastic model of the deep bed filtration and has the characteristic univocity conditions given by relations (4.295) and (4.296). The univocity conditions show that the suspension is only fed at times higher than zero. Indeed, here, we have a constant probability for the input of the microparticles ... 

These relations are often called equations of state because they relate different state properties. Since the variables T, P, and [nj] play this special role of yielding the other thermodynamic properties, they are referred to as the natural variables of G. Further information on natural variables is given in the Appendix of this chapter. In writing partial derivatives, subscripts are omitted to simplify the notation. The second type of interrelations are Maxwell equations (mixed partial derivatives). Ignoring the VdP term, equation 3.1-1 has two types of Maxwell relations ... 

LNA has frequently been used to stabilise duplex structures, but in triplex structures the effect is mixed. Partial substitution of a DNA TFO by LNA increases triplex stability, whilst complete substitution leads to destabilisation. Optimal stabilisation was found with substitution every 2-3 nucleotides of the TFO. The incorporation of LNA into a G-quadruplex structure was shown to alter the orientation of the quadruplex from antiparallel to parallel. ... 

The processing of the raw materials is different for plastic clays and lumpy shale. Plastic clays are crushed, ground, mixed, partially dehydrated and then formed into pellets of different sizes on a granulation table or similar apparatus before being thermally treated (half-wet process). Lumpy raw materials, such as shale, are only ground and, if necessary, classified (dry process) before thermal treatment. Adjustment of the bulk density of the final product to the required value is carried out during the subsequent thermal treatment. 

Pentasa mesalazine. pentazocine [ban,inn.jan,usan] (pentazocine hydrochloride [usan] pentazocine lactate [usan] NSC 107430 Fortagesic Fortral Talwin ) is one of the benzomorphan series and is a (mixed partial p and full k) OPIOID RECEPTOR AGONIST with OPIOID ANALGESIC activity. It is used orally or by injection to treat moderate to severe pain, pentazocine hydrochloride pentazocine, pentazocine lactate pentazocine, pentetrazol [ban, inn] (pentylenetetrazole pentamethylenetetrazole) has similar properties to doxapram as a CNS stimulant and respiratory stimulant. It was previously used intramuscularly to treat barbiturate and other CNS depressants in overdose, and orally for bronchial disorders. 

Note that the first two terms on the right hand side tell us that there is a change in the strain energy density that is incurred because the defect has moved and it has dragged its elastic fields with it. However, these terms do not reflect the presence of broken translational invariance. By exploiting equality of mixed partials, and by rearranging terms via a simple application of the product rule for differentiation, this expression may be rewritten as... 

Fig. 5.30 Selected mixed partially and totally oxidized diphosphanes and their chemical shift values...

A function has an exact differential if its mixed partial derivatives are equal. That is, f(x,y) has an exact... 

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