Survival function

Mohs RC, Doody RS, Morris JC, Ieni JR, Rogers SL, Perdomo CA and Pratt RD (2001). A 1-year, placebo-controlled preservation of function survival study of donepezil in AD patients. Neurology, 57, 481-488. 

Does addition of functions survive the equivalence Does scalar multiplication (by complex numbers) survive the equivalence Does multiplication of two functions survive the equivalence ... 

Sodium benzylselenolate in refluxing DMF is a superior reagent for O-demethylation at the hindered 1-, 8-, and 11-positions of the aporphine nucleus. Methylenedioxy-functions survive the reaction.47 The microbial transformation of glaucine produces mainly norglaucine and predicentrine (25).48... 

One has simply to assume a particular probability distribution for A with the survival function available in a closed form, namely the exponential, Erlang, Rayleigh, and Weibull. Table 9.1 summarizes the probability density functions, survival functions, and hazard rates for the above-mentioned distributions. In these expressions, A is the scale parameter and p and v are shape parameters with k, A, p > 0 and v = 1, 2,.... ... 

Lithium naphthalenide (prepared from lithium and 1.33 equivalents of naphthalene) also reductively cleaves benzyl ethers [Scheme 4.143],262 Some functionalities survive the reaction conditions like carbon-carbon double bonds, benzene rings, THP ethers, stlyl ethers and methoxymethyl ethers. A ketone group can be present but its prior conversion to an enolate is necessary. A similar transformation, but with a catalytic amount of naphthalene, has been reported.263 Although allyl ethers are also cleaved by the procedure, the selective deprotec-... 

A modification of the Oppenauer oxidation which uses trichloroacetaldehyde on alumina provides a good, general oxidation of alcohols, and in particular will oxidize a secondary akdiol in the presence of a primary one, as shown by the examples given in Scheme 16. This method is claimed to be superiw to silver carbonate on Celite and much cheaper. Other advantages of this method are that it is neutral, nonaqueous, and halide, ester and lactone functionalities survive the reaction conditions. ... 

In parallel there exist some attempts trying to introduce a field theory (FT) starting from the standard description in terms of phase space [4—6], Of course, the best way to derive a FT for classical systems should consist in taking the classical limit of a QFT in the same way as the so called classical statistical mechanics is in fact the classical limit of a quantum approach. This limit is not so trivial and the Planck constant as well as the symmetry of wave functions survive in the classical domain (see for instance [7]). Here, we adopt a more pragmatic approach, assuming the existence of a FT we work in the spirit of QFT. 

Whether the inactive region is a true continuum (e.g., photofragmentation) or a quasi-continuum comprised of an enormous density of rigorously bound eigenstates (polyatomic molecule dynamics, Section 9.4.14) is often of no detectable consequence. The dynamical quantities discussed in Section 9.1.4 (probability density, density matrix, autocorrelation function, survival probability, transfer probability, expectation values of coordinates and conjugate momenta) describe the active space dynamics without any reference to the detailed nature of the inactive space. 

Our recently developed Steady State Theory of Mutation Rates has been used to compare the effects of aging and irradiation on the lens of the eye. A set of data for rats, which included animals irradiated by X-rays or neutrons and nonirradiated animals, was used. It was found that functional survival of the organ could be analyzed separately from survival of the animal. Results indicate that at high doses of radiation two cataractogenic mechanisms are operative (1) an early-acting independent mechanism, and (2) an acceleration of the aging mechanism. At lower doses the latter mechanism is dominant. 

Since the steady state theory of mutation rates is basic and thus not limited to a specific application, it should be applicable to many quantal phenomena in biology. In this paper the functional survival of a single organ, the lens of the eye, is considered. 

The functional survival, that is, transparency, of the lens of the eye with increasing age is shown for control animals and for rats irradiated with... 

O-demethylation of aryl methyl ethers of nonphenolic aporphine alkaloids. Regioselective demethylation by this method occurs at positions 1,8, and 11 of the aporphine nucleus methylenedioxy functions survive the reaction (447). Selective cleavage of the methylenedioxy group in O-methyl-bulbocapnine with boron trichloride is discussed in Section III,C (448). The ether cleavage of methoxy- and methylenedioxy-substituted isoquinoline has been reviewed (346). 

In Table 3, a detailed analysis of the orbital expansion coefficients is reported for the subset containing functions of x-type centred on the F nucleus. Again the functions retained in the truncated subsets are indicated by the dots. The numbers of functions in each of the subsets for Too, 6, T5, T4 and T3 are 30, 26, 24, 20 and 17. In each of the truncated sets there are more functions surviving the condition (5) than in the corresponding sets centred on the B nucleus. This reflects the higher nuclear charge in F which necessitates the retention of more contracted primitive functions. 

The inverse Fourier-Laplace transformation of l/(z — E(z)) provides the autocorrelation function (survival probability) represented in Figure 1.4. The... 

Figure 1.12 Modulus of the autocorrelation function (survival probability), c(t), for the initial states given in the caption of Figure 1.11. Full line effective resolvent method dotted line close-coupling.

The exponential dependence on the energy means that the high energy states decay faster than the low energy ones and, in the long (imaginary) time limit, only the ground state wave function survives. 

Once in place, both isopropylidene and benzylidene functionality survive many routine synthetic operations and, when no longer required, may be readily removed by hydrolysis. Two aspects of acetal deprotection are of interest here (1) partial hydrolysis of bis-acetals, particularly bis(isopropylidenes) and (2) protecting group interchange, particularly of benzylidenes. 

Carotid bodies have also been transplanted into the previously damaged striatum of monkeys (27). The idea was to replace central dopaminergie neurons by glomus cells, capable of reestablishing dopaminergic function. Survival of tyrosine... 

The separated 3D wave equation can no longer describe any of these fundamental rotations. For this reason, the discovery of electron spin necessitated its introduction into quantum theory as another ad hoc postulate. The anomalous consequence is the unphysical situation of a point particle with spin. Only part of the spin function survives solution of the 3D wave equation, in the form of a complex variable interpreted as orbital angular momentum. In the so-called / -state, it has the peculiar property of non-zero orbital angular momentum with zero component in the direction of an applied magnetic field. This is the price to pay for elimination of spherical rotation. 

Ethoxy-, -chloro- and -phenoxy-pyridine 1-oxides give 2-hydroxypyridine 1-oxide, the oxide function surviving in these cases" . An unusual example is that of 2-carboxy-5-methoxycarbonylpyridine 1-oxide. With benzoyl chloride in dioxan this gives 6-hydroxynicotinic acid. However, with acetic anhydride or acetyl chloride, methyl 4-acetoxynicotinate results . 

Because the hydrogenolysis of the phenylmethyl (benzyl) ether in the final step occurs under neutral conditions, the tertiary alcohol function survives untouched. A tertiary butyl ether would have been a worse choice as a protecting group, because cleavage of its carbon-oxygen bond would have required acid (Section 9-8), which may cause dehydration (Section 9-2). 

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