We set a control model to study the biomechanical problem of swing pumping. After describing the sytem, we provide the solution to some optimal control problems.

We consider the problem of two bodies rolling one on each other. A quantization in introduced by means of the selection of base points and paths on one of the body. The reachability and path planning problem is considered.

In this paper we are concerned with the pointwise behaviour of functions in certain classes of weakly differentiable functions. We focus on first order Orlicz-Sobolev spaces and we establish optimal theorems of Rademacher type and of approximate differentiability type in this setting.

To produce grids conforming to the boundary of a physical domain with boundary orthogonality features, algebraic methods like transfinite interpolating schemes can be profitably used. Moreover, the coupling of Hermite-type (also interpolating prescribed boundary direction) schemes with elliptic methods turns out to be effective to overcome the drawback of both algebraic and elliptic strategies. Thus, in this paper, we present an algorithm for the generation of boundaryorthogonal grids which couples a mixed Hermite algebraic method with a boundaryorthogonalelliptic scheme. Numerical tests on domains with classical geometries show satisfactory performances of the algorithm and coupling effectiveness in achieving grid boundary orthogonality and smoothness.

We study the inverse problem of determining the position of the moving C-terminal domain in a metalloprotein from measurements of its mean paramagnetic tensor $\bar\chi$. The latter can be represented as a finite sum involving the corresponding magnetic susceptibility tensor $\chi$ and a finite number of rotations. We obtain an optimal estimate for the maximum probability that the C-terminal domain can assume a given orientation, and we show that only three rotations are required in the representation of $\bar\chi$, and that in general two are not enough.

The paper gives a contribution of wavelet aspects to classical algebraic polynomial approximation theory. Algebraic polynomial interpolating scaling functions and wavelets are constructed by using the interpolating properties of de la Vallée Poussin kernels w.r.t. the four kinds of Chebyshev weights. For the decomposition and reconstruction of a given function the structure of the involved matrices is studied in order to reduce the computational effort by means of fast cosine and sine transforms.

In this paper the definition of semiseparable matrices is investigated. Properties of the frequently used definition and the corresponding representation by generators are deduced. Corresponding to the class of tridiagonal matrices another definition of semiseparable matrices is introduced preserving the nice properties dual to the class of tridiagonal matrices. Several theorems and properties are included showing the viability of this alternative definition. Because of the alternative definition, the standard representation of semiseparable matrices is not satisfying anymore. The concept of a representation is explicitly formulated and a new kind of representation corresponding to the alternative definition is given. It is proved that this representation keeps all the interesting properties of the generator representation.

An algorithm to reduce a symmetric matrix to a similar semiseparable one of semiseparability rank 1, using orthogonal similarity transformations, is proposed in this paper. It is shown that, while running to completion, the proposed algorithm gives information on the spectrum of the similar initial matrix. In fact, the proposed algorithm shares the same properties of the Lanczos method and the Householder reduction to tridiagonal form. Furthermore, at each iteration, the proposed algorithm performs a step of the QR method without shift to a principal submatrix to retrieve the semiseparable structure. The latter step can be considered a kind of subspace-like iteration method, where the size of the subspace increases by one dimension at each step of the algorithm. Hence, when during the execution of the algorithm the Ritz values approximate the dominant eigenvalues closely enough, diagonal blocks will appear in the semiseparable part where the norm of the corresponding subdiagonal blocks goes to zero in the subsequent iteration steps, depending on the corresponding gap between the eigenvalues. A numerical experiment is included, illustrating the properties of the new algorithm.

The QR algorithm is one of the classical methods to compute the eigendecomposition of a matrix. If it is applied on a dense n x n matrix, this algorithm requires O(n^3) operations per iteration step. To reduce this complexity for a sytmmetric matrix to O(n), the original matrix is first reduced to tridiagonal form using orthogonal similarity transformations. In the report (Report TW360, May 2003) a reduction from a symmetric matrix into a similar semiseparable one is described. In this paper a QR algorithm to compute the eigenvalues of semiseparable matrices is designed where each iteration step requires O(n) operations. Hence, combined with the reduction to semiseparable form, the eigenvalues of symmetric matrices can be computed via intermediate semiseparable matrices, instead of tridiagonal ones. The eigenvectors of the intermediate semiseparable matrix will be computed by applying inverse iteration to this matrix. This will be achieved by using an O(n) system solver, for semiseparable matrices. A combination of the previous steps leads to an algorithm for computing the eigenvalue decompositions of semiseparable matrices. Combined with the reduction of a symmetric matrix towards semiseparable fortri, this algorithm can also be used to calculate the eigenvalue decomposition of symmetric matrices. The presented algorithm has the same order of complexity as the tridiagonal approach, but has larger lower order terms. Numerical experiments illustrate the complexity and the numerical accuracy of the proposed method.

The linear space of all proper rational functions with prescribed poles is considered. Given a set of points in the complex plane and the weights, we define the discrete inner product. In this paper we derive a method to compute the coefficients of a recurrence relation generating a set of orthonormal rational basis functions with respect to the discrete inner product. We will show that these coefficients can be computed by solving an inverse eigenvalue problem for a matrix having a specific structure. In the case where all the points lie on the real line or on the unit circle, the computational complexity is reduced by an order of magnitude.

The authors consider the generalized airfoil equation in some weighted Holder-Zygmund spaces with uniform norms. Using a projection method based on the de la Vallée Poussin interpolation, they reproduce the estimates of the L2 case by cutting off the typical extra log m factor which seemed inevitable to have dealing with uniform norm, because of the unboundedness of the Lebesgue constants. The better convergence estimates do not produce a greater computational effort: the proposed numerical procedure leads to solve a simple tridiagonal linear system, the condition number of which tends to a finite limit as the dimension of the system tends to infinity, whatever natural matrix norm is considered. Several numerical tests are given.

We simulate the progression of the HIV-1 infection in untreated host organisms. The phenotype features of the virus are represented by the replication rate, the probability of activating the transcription, the mutation rate and the capacity to stimulate an immune response (the so-called immunogenicity). It is very difficult to study in \emph{in-vivo} or \emph{in-vitro} how these characteristics of the virus influence the evolution of the disease. Therefore we resorted to simulations based on a computer model validated in previous studies. We observe, by means of computer experiments, that the virus continuously evolves under the selective pressure of an immune response whose effectiveness downgrades along with the disease progression. The results of the simulations show that immunogenicity is the most important factor in determining the rate of disease progression but, by itself, it is not sufficient to drive the disease to a conclusion in all cases.

This work presents the first results of an experiment aiming to derive a high resolution Digital Terrain Model (DTM) by kinematic GPS surveying. The accuracy of the DTM depends on both the operational GPS precision and the density of GPS samples. The operational GPS precision, measured in the field, is about 10 cm. A Monte Carlo analysis is performed to study the dependence of the DTM error on the sampling procedure. The outcome of this analysis is that the accuracy of the topographic reconstruction is less than 1 m even in areas with a density of samples as low as one sample per 100 m(2), and becomes about 30 cm in areas with at least one sample per 10 m2. The kinematic GPS technique gives a means for a fast and accurate mapping of terrain surfaces with an extension of a few km(2). Examples of application are the investigation of archaeological sites and the stability analysis of landslide prone areas.