Difference derivative central

Thus, the right and left difference derivatives generate approximations of order 1 to Lu = u, while the central difference derivative approximates to the second order the same. 

Since the central difference derivative in t approximates to the second order in r and Au = -f 0 h ), scheme (53) approximates... 

The natural replacement of the central difference derivative u x) by the first derivative Uo leads to a scheme of second-order approximation. Such a scheme is monotone only for sufficiently small grid steps. Moreover, the elimination method can be applied only for sufficiently small h under the restriction h r x) < 2k x). If u is approximated by one-sided difference derivatives (the right one for r > 0 and the left one % for r < 0), we obtain a monotone scheme for which the maximum principle is certainly true for any step h, but it is of first-order approximation. This is unacceptable for us. 

In addition to the central difference derivative, code is included for a right-difference formulation rderiv() in lines 23 through 41. This is similar to the central difference formulation but uses only a two point differencing equation and... 

Subroutine FUNDR. This subroutine calculates the required derivatives for REGRES by central difference, using EVAL to calculate the objective functions. 

Third card FORMAT(8F10.2), size of increments to be used in central difference formula for calculating derivatives with respect to the independent variables. 

TRANSFER VECTOR FOR PARAMETERS VECTOR OF CENTRAL DIFFERENCE INCREMENTS FOP CALCULATING DERIVATIVES WRT THE PARAMETERS VECTOR OF CENTRAL DIFFERENCE INCREMENTS FOR... 

If we write the time-dependent Sclnodinger equation as 5i i/(T = -(i/li)f7i i, then, after replacing the time derivative by a central difference, we obtain... 

The leap-frog algorithm uses the simplest central difference I or-m n la for a derivative... 

The Michael reaction is of central importance here. This reaction is a vinylogous aldol addition, and most facts, which have been discussed in section 1.10, also apply here the reaction is catalyzed by acids and by bases, and it may be made regioselective by the choice of appropriate enol derivatives. Stereoselectivity is also observed in reactions with cyclic educts. An important difference to the aldol addition is, that the Michael addition is usually less prone to sterical hindrance. This is evidenced by the two examples given below, in which cyclic 1,3-diketones add to o, -unsaturated carbonyl compounds (K. Hiroi, 1975 H, Smith, 1964). 

The PBRis distinct from the central BZ receptor although both can be present in the same tissues in differing ratios. PBRs are predominately localized on the outer mitochondrial membrane and are thus intracellular BZ recognition sites. The PBR is composed of three subunits an 18,000 mol wt subunit that binds isoquinoline carboxamide derivatives a 30,000 mol wt subunit that binds BZs and a 32,000 mol wt voltage-dependent anion channel subunit. The porphyrins may be endogenous ligands for the PBR. PBRs are involved in the control of cell proliferation and differentiation and steroidogenesis. 

In the ketone method, the central carbon atom is derived from phosgene (qv). A diarylketone is prepared from phosgene and a tertiary arylamine and then condenses with another mole of a tertiary arylamine (same or different) in the presence of phosphoms oxychloride or zinc chloride. The dye is produced directly without an oxidation step. Thus, ethyl violet [2390-59-2] Cl Basic Violet 4 (15), is prepared from 4,4 -bis(diethylamino)benzophenone with diethylaruline in the presence of phosphoms oxychloride. This reaction is very useful for the preparation of unsymmetrical dyes. Condensation of 4,4 -bis(dimethylamino)benzophenone [90-94-8] (Michler s ketone) with AJ-phenjl-l-naphthylamine gives the Victoria Blue B [2580-56-5] Cl Basic Blue 26, which is used for coloring paper and producing ballpoint pen pastes and inks. 

Research for an antidepressant among non-tricyclic compounds with pharmacological effects qualitatively different from those of the conventional tricyclic compounds led to the preparation and testing of a series of indazole derivatives for reserpine-like activity in mice. l-[3-(Dimethylamino)propyl]-5-methyl-3-phenyl-l//-indazole (FS-32 692) antagonizes reserpine-induced effects and potentiates amphetamine-induced self-stimulation and l-Dopa-induced increase in motor activity. FS-32 produces an anticholinergic action mainly on the central nervous System, while the action of imipramine occurs centrally as well as peripherally (79AF511). 

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