THE BIOLOGY OF THE (6–4) PHOTOPRODUCT

The (6-4) photoproduct is an important determinant of the lethal and mutagenic effects of UV irradiation of biological systems. The removal of this lesion appears to correlate closely with the early DNA repair responses of mammalian cells, including DNA incision events, repair synthesis and removal of replication blocks. The processing of (6-4) photoproducts and cyclobutane dimers appears to be enzymatically coupled in bacteria and most mammalian cell lines examined (i.e. a mutation affecting the repair of one lesion also often affects the other), although exceptions exist in which repair capacity may be evident for one photoproduct and not the other (e.g. UV61 and the XP revertant cell line). These differences in the processing of the two photoproducts in some cell lines of human and rodent origin suggest that in mammalian cells, different pathways for the repair of (6-4) photoproducts and cyclobutane dimers may be used. This observation is further supported by pleiotropic repair phenotypes such as those observed in CHO complementation class 2 mutants (e.g., UV5, UVL-1, UVL-13, and V-H1). Indirect data, from HCR of UV irradiated reported genes and the cytotoxic responses of UV61, suggest that the (6-4) photoproduct is cytotoxic in mammalian cells and may account for 20 to 30% of the cell killing after UV irradiation of rodent cells. Cytotoxicity of the (6-4) photoproduct may be important in the etiology of sunlight-induced carcinogenesis, affecting mutagenesis as well as tumorigenesis. The intricate photochemistry of the (6-4) photoproduct, its formation and photoisomerization, is in itself extremely interesting and may also be relevant to sunlight carcinogenesis. The data reviewed in this article support the notion that the (6-4) photoproduct and its Dewar photoisomer are important cytotoxic determinants of UV light. The idea that the (6-4) photoproduct is an important component in the spectrum of UV-induced cytotoxic damage may help clarify our understanding of why rodent cells survive the effects of UV irradiation as well as human cells, without apparent cyclobutane dimer repair in the bulk of their DNA. The preferential repair of cyclobutane dimers in essential genes has been proposed to account for this observation (Bohr et al., 1985, 1986; Mellon et al., 1986). The data reviewed here suggest that understanding the repair of a prominent type of noncyclobutane dimer damage, the (6-4) photoproduct, may also be important in resolving this paradox.     

Turning Point Problems and Resonance

Consider the boundary value problem: ²yⁿ + (xp(x) + ²f(x, ))y'+ g(x, )y = 0, y(a) = A, y(b) = B, where a < 0 < b, p(x)< p(x) < 0, and p, f, and g are analytic. We investigatethe solution of this problem for small positive values of theparameter . If-g(0, 0)/p(0) c where c N = {0, 1, 2, 3,...},then so-called resonance does not occur, and y = o(ⁿ) on closedsubintervals of (a, b), for any n N, with expected boundarylayer behaviour at the end-points. If -g(0, 0)/p(0) = c, c N, then further transformations of dependent and independentvariables may still expose resonance or non-resonance. The setof necessary conditions that is developed is compared to otherauthors' criteria, most notably, Olver's sufficiency condition,and the necessary conditions of Cook & Eckhaus, Lakin, andMatkowsky. Finally, it is proved that these conditions are necessaryfor resonance.     

Crystal Transformation of Nylon 11 Using in situ WAXD

Nylon I I is a high-performance semicrystalline polymer which was used widely in manyfields. In recent years, the curious ferroelectric and piezoelectric propel'ties of nylon I Iwere foundl'2. It is well known that piezoelectricity is related to the crystal form ofNylon I 1.The sample was mounteds in a capillary (diameter was Zmm) within a small ovenwith mica windows. The scattered intensity was recorded from Q = 0.2 to 6.5 A-] (Q =ursine/~) using steps of AQ=o.o5A-'. The values of the p…     

AN INVESTIGATION OF STABILITY IN THE LARGE BEHAVIOUR OF A CONTROL SURFACE WITH STRUCTURAL NON-LINEARITIES IN SUPERSONIC FLOW

It is well known that the presence of non-linearities may significantly affect the aeroelastic response of an aerospace vehicle structure. In this paper, the aeroelastic behaviour at high Mach numbers of an all-moving control surface with a non-linearity in the root support is investigated. Very often, a stable equilibrium point, corresponding to zero displacement of the structure, together with an unstable limit cycle arising from a sub-critical Hopf bifurcation results from the presence of the non-linearity. The stable equilibrium point will then possess a domain of attraction. In this paper, this situation is investigated by first applying the averaging method to obtain a new set of aeroelastic equations in which the limit cycle is replaced by an unstable equilibrium point. A fourth order power series approximation to the stable manifold in the neighbourhood of this equilibrium point is then determined. From the stable manifold, predictions of the domain of attraction of the stable equilibrium point may then be made. The method is applied to two examples in which the non-linearity in the root support was due to either a cubic hardening restoring moment or the presence of freeplay. The approximation to the stable manifold was sufficient to enable significant information about the domain of attraction of the stable equilibrium point of the control surface to be obtained; agreement with predictions from numerical integration of the aeroelastic equations in the time domain was shown to be generally good in the cases considered, though outside the region of validity of the stable manifold expansion, discrepancies will occur. The averaging method was shown to be sufficiently accurate for this analysis even when the non-linearities could not be considered as weak.     

On the Structure of Alternating Direction Implicit (A.D.I.) and Locally One Dimensional (L.O.D.) Difference Methods

The general structure of A.D.I. and L.O.D. difference schemesis considered with regard to their construction for time dependentproblems in two and three space dimensions. By considering approximationsto exp {k(L+M)} where L and M are differential operators inthe space variables and k is the time step, we show how severalknown schemes can be viewed as having come from this type ofapproximation. In addition several new schemes based on thistype of approximation are suggested. The arguments used areentirely informal and no attempt is made to prove the stabilityor convergence of the various schemes. Our aim is merely topoint out a possible structure for the generation of A.D.I.and L.O.D. difference schemes.     

A High Accuracy Alternating Direction Method for the Wave Equation

The alternating direction implicit (ADI) method of Lees forsolving the wave equation in two space dimensions is generalizedand an ADI method of increased accuracy obtained. The new methodis demonstrated by a numerical example. An extension is alsogiven to cover the case of the wave equation in three spacedimensions.     

An Exact Boundary Technique for Improved Accuracy in the Finite Element Method

Discretization procedures such as the finite difference andfinite element methods for the solution of elliptic equationswith Dirichlet boundary conditions suffer in general from thedefect that for a given grid size, the solution is influencedonly by a limited amount of the boundary data. Here blendingfunction interpolants (Gordon, 1971) are used to construct anoverall interpolant for a closed region which matches all theboundary information on the perimeter of the region for anyvalue of the grid spacing. This overall interpolant is incorporatedinto the Ritz Galerkin version of the finite element methodand error estimates obtained for this improved procedure. Twonumerical examples are given which demonstrate the increasedaccuracy of the exact boundary scheme as compared with the discretizedboundary scheme, and as expected, the improvement is particularlynoticeable when the number of elements is small.