Antibody-antigen interaction on polystyrene: an in situ ellipsometric study

The objective of this investigation was to monitor the adsorption of antibodies to polystyrene surfaces using ellipsometry. Commercial polystyrene slides used for solid state diagnostics were selected as substrates and the adsorption of three different antibodies (human IgG, bovine IgG and goat anti-human IgG) were evaluated. Based on theoretical models describing the ellipsometric data, it was concluded that the adsorption of antibodies should result in layers that are sufficiently thick to be able to monitor the adsorption in terms of adsorbed amount and thickness of the layer with a reasonable precision. The experimental results confirmed this assumption and values of 2.0-2.3 mg/m(2) were detected for the adsorbed amount with a corresponding thickness of 10-16 nm. It was furthermore found that the antibodies bound irreversibly with respect to rinsing with protein-free solutions. In additional experiments, the consecutive incubation of human IgG and anti-human IgG was investigated. These results showed that, on average, approximately half of the surface immobilized anti-human IgG molecules are capable of binding to human IgG during its incubation. From the consecutive binding experiments it could also be concluded that antibodies present in the polyclonal anti-human IgG preparation were capable of binding to around four different epitopes on the human IgG. A final set of experiments addressed the stability of adsorbed human IgG layers with respect to drying and incubation with surfactant. The results revealed that the adsorbed antibody layer is relatively resistant to these treatments.     

On kernels of perfect codes

It is shown that there exists a perfect one-error-correcting binary code with a kernel which is not contained in any Hamming code.     

A Probabilistic Technique for Finding Almost-Periods of Convolutions

We introduce a new probabilistic technique for finding ‘almost-periods’ of convolutions of subsets of groups. This gives results similar to the Bogolyubovtype estimates established by Fourier analysis on abelian groups but without the need for a nice Fourier transform to exist. We also present applications, some of which are new even in the abelian setting. These include a probabilistic proof of Roth’s theorem on three-term arithmetic progressions and a proof of a variant of the Bourgain–Green theorem on the existence of long arithmetic progressions in sumsets A+B that works with sparser subsets of {1, . . . , N} than previously possible. In the non-abelian setting we exhibit analogues of the Bogolyubov–Freiman–Halberstam–Ruzsa-type results of additive combinatorics, showing that product sets A ₁ · A ₂ · A ₃ and A ² · A ⁻² are rather structured, in the sense that they contain very large iterated product sets. This is particularly so when the sets in question satisfy small-doubling conditions or high multiplicative energy conditions. We also present results on structures in A · B.     

Well-Posed State/Signal Systems in Continuous Time

We introduce a new class of linear systems, the L ^p -well-posed state/signal systems in continuous time, we establish the foundations of their theory and we develop some tools for their study. The principal feature of a state/signal system is that the external signals of the system are not a priori divided into inputs and outputs. We relate state/signal systems to the better-known class of well-posed input/state/output systems, showing that state/signal systems are more flexible than input/state/output systems but still have enough structure to provide a meaningful theory. We also give some examples which point to possibilities for further study.     

Optical map transformations

An optical technique for performing general types of map transformations is introduced. Using a coherent system, the object distribution is multiplied by a phase function so that its frequency spectrum constitutes the transformation wanted. Also shown is how imaging systems can be made space variant. Computer-generated holograms are used to give examples of optical arrangements and experimental results.     

Correlated flipping of four benzene rings in substituted [2.2.2.2]Paracyclophanetetraenes

Dynamic NMR spectroscopy and molecular mechanics calculations show that the flipping of the four benzene binge in certain substituted [2.2.2.2]paracyclophanetetraenes occurs in a correlated fashion.     

Balancing Neumann‐Neumann methods for incompressible Stokes equations

Balancing Neumann‐Neumann methods are introduced and studied for incompressible Stokes equations discretized with mixed finite or spectral elements with discontinuous pressures. After decomposing the original domain of the problem into nonoverlapping subdomains, the interior unknowns, which are the interior velocity component and all except the constant‐pressure component, of each subdomain problem are implicitly eliminated. The resulting saddle point Schur complement is solved with a Krylov space method with a balancing Neumann‐Neumann preconditioner based on the solution of a coarse Stokes problem with a few degrees of freedom per subdomain and on the solution of local Stokes problems with natural and essential boundary conditions on the subdomains. This preconditioner is of hybrid form in which the coarse problem is treated multiplicatively while the local problems are treated additively. The condition number of the preconditioned operator is independent of the number of subdomains and is bounded from above by the product of the square of the logarithm of the local number of unknowns in each subdomain and a factor that depends on the inverse of the inf‐sup constants of the discrete problem and of the coarse subproblem. Numerical results show that the method is quite fast; they are also fully consistent with the theory. © 2002 John Wiley & Sons, Inc.     

Rational carrier-period for binarization of sampled images and holograms

Introduction of a rational period in dither methods to binarize graytone images offers an additional degree of freedom. This can be used to overcome the inevitable tradeoff between graytone reproduction and detail resolution in these techniques. The concept is demonstrated with a one-dimensional triangular-shaped carrier function. Experimental results are shown.