Generalised Dirichelt-to-Neumann map in time dependent domains

We study the heat, linear Schrodinger and linear KdV equations in the domain l(t) < x < ∞, 0 < t < T, with prescribed initial and boundary conditions and with l(t) a given differentiable function. For the first two equations, we show that the unknown Neumann or Dirichlet boundary value can be computed as the solution of a linear Volterra integral equation with an explicit weakly singular kernel. This integral equation can be derived from the formal Fourier integral representation of the solution. For the linear KdV equation we show that the two unknown boundary values can be computed as the solution of a system of linear Volterra integral equations with explicit weakly singular kernels. The derivation in this case makes crucial use of analyticity and certain invariance properties in the complex spectral plane. The above Volterra equations are shown to admit a unique solution.

Interactive effect of cowpea variety, dose and exposure time on bruchid tolerance to botanical pesticides

Callosobruchus maculatus has for years remained a serious menace in cowpea in Sub-Sahara Africa. The objective of this study was to investigate the effect of genotypic cowpea (Vigna unguiculata (L.) Walp) varieties, time and dose on C. maculatus exposed to powders of Piper guineense and Eugenia aromatica. Irrespective of duration and botanicals, bruchid reared on KDV showed the highest tolerance to both plant materials; while their counterparts from IAR48V were the most susceptible. Median lethal time (LT50) also varied according to the plant materials; with the highest in KDV reared bruchid [P. guineense: KDV (18.31), IAR48V (9.27), IFBV (13.17); E. aromatica: KDV (76.01), IAR48V (5.59), IFBV (6.49)]. There was a significant impact of cowpea variety (V), exposure time (T) and dose (D) on the tolerance of C. maculatus to both plant materials. The effect of all two-way (VxT, VxD, DxT) and three way interactions (V×T×D) on the tolerance of C. maculatus to both plant materials was also significant. Varietal effect was more pronounced in bruchids exposed to E. aromatica; while exposure time was more pronounced in bruchids exposed to P. guineense.

A Variance-Minimizing Filter for Large-Scale Applications

A truly variance-minimizing filter is introduced and its per for mance is demonstrated with the Korteweg– DeV ries (KdV) equation and with a multilayer quasigeostrophic model of the ocean area around South Africa. It is recalled that Kalman-like filters are not variance minimizing for nonlinear model dynamics and that four - dimensional variational data assimilation (4DV AR)-like methods relying on per fect model dynamics have dif- ficulty with providing error estimates. The new method does not have these drawbacks. In fact, it combines advantages from both methods in that it does provide error estimates while automatically having balanced states after analysis, without extra computations. It is based on ensemble or Monte Carlo integrations to simulate the probability density of the model evolution. When obser vations are available, the so-called importance resampling algorithm is applied. From Bayes’ s theorem it follows that each ensemble member receives a new weight dependent on its ‘ ‘distance’ ’ t o the obser vations. Because the weights are strongly var ying, a resampling of the ensemble is necessar y. This resampling is done such that members with high weights are duplicated according to their weights, while low-weight members are largely ignored. In passing, it is noted that data assimilation is not an inverse problem by nature, although it can be for mulated that way . Also, it is shown that the posterior variance can be larger than the prior if the usual Gaussian framework is set aside. However , i n the examples presented here, the entropy of the probability densities is decreasing. The application to the ocean area around South Africa, gover ned by strongly nonlinear dynamics, shows that the method is working satisfactorily . The strong and weak points of the method are discussed and possible improvements are proposed.