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.

We generalize a result of Dar{\'o}czy and K{\'a}tai, on the characterization of univoque numbers with respect to a non-integer base \cite{DarKat95} by relaxing the digit alphabet to a generic set of real numbers. We apply the result to derive the construction of a B\"uchi automaton accepting all and only the greedy sequences for a given base and digit set. In the appendix we prove a more general version of the fact that the expansion of an element $x\in \QQ(q)$ is ultimately periodic, if $q$ is a Pisot number.

We study the L^2 stability of a classical solution of the one-dimensional energy transport model for semiconductors on the whole rel line, under the assumption that the thermodynamic variables remain bounded. The solution converges asymptotically in time to a state in thermodynamic equilibrium.

The discrete Fourier transform of even complex sequences involves, in matrix formulation, a cosine matrix and, in the same way, the discrete Fourier transform of odd complex sequences is related with a sine matrix. Using structural characteristics of the two matrices, whose order is half the length of the symmetric input data, some recursive expressions of them will be constructed. Unlike the previous classical forms of the discrete Fourier transform of an even or odd real vector, the recursive terms in the matrix expressions derived here only involve the same cosine and sine matrices, with halved order. That is, it is shown that, as for the FFT of a general complex sequence, a divide and conquer approach can also be used to compute the DFT of even or odd sequences. The recursion is closed in the family of the sine and cosine matrices used to describe the DFT of even and odd sequences and no other kind of sine or cosine based matrices are required in recursive terms. Although the obtained results give a new theoretical view on the problem of computing the DFT of even and odd complex sequences, these are not of immediate practical use since the computational cost is higher than other currently employed algorithms. Copyright © 2005 John Wiley & Sons, Ltd.

A new fast iterative algorithm is proposed to denoise images affected by Gaussian additive noise, by solving a constrained optimization problem. A family of functionals parameterized by a few hyperparameters already proposed in the literature to solve denoising problems is considered. The algorithm estimates jointly the image and the hyperparameters, therefore providing an automatic method. Each member of the family is made up of a coherence with the data term and a term enforcing a roughness penalty and preserving jump discontinuities. Assuming we know the noise variance, an adequacy constraint is also considered. The algorithm computes a member of the family and a minimizer of it which satisfies the constraint. A convergence proof is provided. We then consider a heuristic version of the algorithm which gives restorations of comparable quality whose computational complexity is a linear function of the pixels number. Experimental results on synthetic and real data are presented. Moreover, numerical comparisons with several fast denoising methods are provided.

Marine phytoplankton are known to produce surface-active materials as part of their metabolism. The surface tension gradient due to the presence of plankton-produced surfactants leads to a surface shear stress, commonly known as Marangoni stress. In this work we try to gain some understanding on these complex phenomena while, at the same time, obtaining some information on the order of magnitude of the surface stress and the resulting velocity in the bulk flow. As the direct modelling of the surfactants is extremely difficult due to the complexity (and uncertainty) of their chemical composition and to the absence of information on the rate of production by marine phytoplankton, we have formulated a model of their effects based on the data of surface activity of seawater samples as they are presented by ?uti? et al. (1981) [?uti?, V., ?osovi?, B., Mar?enko, E., Bihari, N., 1981. Surfactant production by marine phytoplankton. Mar. Chem. 10, 505-520] and ?uti? and Legovic (1990) [?uti?, V., Legovic, T., 1990. Relationship between phytoplankton blooms and dissolved organic matter in the Northern Adriatic. In: Final reports on research projects dealing with eutrophication and plankton blooms (activity h). Mediterranean Action Plan (MAP) Technical Reports Series No. 37. United Nations Environment Program (UNEP), Athens]. Using satellite data and a chlorophyll concentration profile reported in the literature we predict a Marangoni stress whose maximum order of magnitude is 10- 6 N m- 2. We also present the results of a numerical test, where we evaluate the Marangoni stress caused by horizontal variations of the plankton distribution due to the converging flows in a thermal bar, obtaining a Marangoni stress of order of magnitude 10- 5 N m- 2 and a corresponding velocity in the bulk that is at most equal to 10- 4 m s- 1, with values of film pressure within the range of the data available in the literature.

This paper presents two examples of application of Synthetic Aperture Radar (SAR) interferometry (InSAR) to typical geomorphological problems. The principles of InSAR are introduced, taking care to clarify the limits and the potential of this technique for geomorphological studies. The application of InSAR to the quantification of landform, attributes such as the slope and to the estimation of landform variations is investigated. Two case studies are presented. A first case study focuses on the problem of measuring landform attributes by interferometric SAR data. The interferometric result is compared with the corresponding one obtained by a Digital Elevation Model (DEM). In the second case study, the use of InSAR for the estimation of landform variations caused by a landslide is detailed. (c) 2004 Elsevier B.V. All rights reserved.

Our paper describes an example of how new sophisticated applications can be introduced to support the management of large and widely distributed organizations belonging to the Public Sector and in particular to Research, Development and Education. We present SIGLA, the integrated planning and financial accounting system developed and maintained by CNR (the Italian National Research Council) in order to support the financial resource management process, from guideline and objective definition, to budget production and result verification. This application allows strict control of the actual financial resource usage and a crosscheck between objectives and results of research activities. The design and implementation of the system started at the end of the year 2000 and the system is still evolving, following the re-organization of the Council. We start with a brief description of the circumstances which lead to re-defining CNR's organizational model and thus to designing and implementing CNR's new financial accounting system from scratch. We then provide an overview of the organizational model supported by the application. Afterwards we describe the application in terms of code metrics, programming languages, high level inputs and outputs, technology platforms, documentation and hosting environment. An important point in successfully introducing complex tools into a large organization like CNR is to ensure fast learning of the basic (and possibly the advanced) functionalities. Exhaustive documentation is surely a good asset but may not be sufficient, especially when time is a critical factor. In the paper we describe the training strategy we established, mainly based on tutorials and distance learning tools. Last but not least, we present the structure of the helpdesk service which supports users in their daily routine. We conclude the paper with the description of our field experience in running the application and some remarks about SIGLA's reusability.