Degenerate variables

In most SBH experiments, probe sets are deliberately designed to improve discrimination. The use of probes shorter than 25 bases inherently enhances discrimination. In addition, SBH experiments may use probe molecules with an informative oligomer core of length n surrounded by a few degenerate (variable) bases, e.g. N j-B -N, which helps enhance discrimination [12,19,31]. Using degenerate bases to surround a fixed oligomer core minimizes the problem of end mismatch discrimination because the fixed core is internalized within the probe. 

The non-degenerate variables satisfy the same Hamilton equations of the Hamiltonian system considered in Figure 4, with perturbing parameter... 

We now couple the non-degenerate and degenerate variables by considering the Hamiltonian ... 

The M a s and Ja s we call proper angle and action variables, the wp and J/s improper or degenerate variables the w s remain constant during the motion. The number s of the independent frequencies va is called the degree of periodicity of the system. 

In order that the division into non-dcgencrate and degenerate variables may persist, the wjs must not depend on the wa s or the id s on the w s. This means, however, that the r s vanish. The transfor-... 

Suffixes p and a both refer to accidentally degenerate variables.) This is a partial differential equation of the Hamilton-Jacobi type. It does not admit of integration in all cases, and the method fails, therefore, for the determination of the motion for arbitrary values of the Jfc s. We can show, however, as in the example of 44, that the motions for which the wp° s are constant to zero approximation, and remain constant also to a first approximation, are stationary motions in the sense of quantum theory. 

Special cases, in which, for example, by averaging over the nondegenerate variables, their dependence on the degenerate variables disappear (e.g. H1=0), must of course be examined separately. 

We note here that the qiiantnm levels denoted by the capital indices I and F may contain numerous energy eigenstates, i.e. are highly degenerate, and refer to chapter A3.4 for a more detailed discussion of these equations. The integration variable in equation (A3.13.9) is a = 7 j / Ic T. 

To extend the above kinetie model to this more general ease in whieh degenerate levels oeeur, one uses the number of moleeules in eaeh level (N and Nf for the two levels in the above example) as the time dependent variables. The kinetie equations then governing their time evolution ean be obtained by summing the state-to-state equations over all states in eaeh level... 

The solutions for the unperturbed Hamilton operator from a complete set (since Ho is hermitian) which can be chosen to be orthonormal, and A is a (variable) parameter determining the strength of the perturbation. At present we will only consider cases where the perturbation is time-independent, and the reference wave function is non-degenerate. To keep the notation simple, we will furthermore only consider the lowest energy state. The perturbed Schrodinger equation is... 

Accounting for this effect, it was possible to apply dynamic NMR spectroscopy to measure energy barriers to the prototropic rearrangements of pyrazoles. Temperature-variable spectra of a series of 4-substituted pyra-zoles 5 and 6 have been studied in methanol-d4 solutions and the free energy barriers of the degenerate type 2a 2b tautomerization reported (93CJC1443). 

An estimate of the energy barrier to the degenerate tautomerization 26a 26b of 1,2,4-triazole has been obtained from temperature-variable... 

As might be predicted from these similarities between PNS and CNS, many disease entities can affect both these tissues. It should be noted, however, that the clinical expression of such diseases is variable and is sometimes restricted to the PNS. For example, patients with thiamine deficiency may display symmetrical distal sensorimotor polyneuropathy without accompanying CNS degeneration. Untreated infection with human immunodeficiency virus (HIV) may cause early polyneuropathy, with dementia appearing months or years later. Similarly, patients with sulfatidase deficiency or adrenoleukodystrophy may present initially with polyneuropathy, while their CNS dysfunction remains clinically undetectable. 

Disorders of glutathione Defective synthesis of glutathione, the major intracellular antioxidant Spinocerebellar degeneration, mental retardation, cataracts, hemolysis. Severe acidosis in some cases N-acetylcysteine (variable response)... 

EPA has derived a chronic oral RfD of 0.001 mg/kg/day for hexachloroethane (IRIS 1995). This value is based on a NOAEL of 1 mg/kg/day for atrophy and degeneration of the renal tubules in rats exposed for 16 weeks (Gorzinski et al. 1985). The NOAEL was divided by an uncertainty factor of 1,000 to account for interspecies extrapolation, human variability, and the use of a subchronic study. EPA places medium confidence in this RfD (IRIS 1995). 

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