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Mathematical Methods (mathematical + methods)
Selected AbstractsAsymptotic and spectral analysis of non-selfadjoint operators generated by a filament model with a critical value of a boundary parameterMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2003Marianna A. Shubov Abstract We consider a class of non-selfadjoint operators generated by the equation and the boundary conditions, which govern small vibrations of an ideal filament with non-conservative boundary conditions at one end and a heavy load at the other end. The filament has a non-constant density and is subject to a viscous damping with a non-constant damping coefficient. The boundary conditions contain two arbitrary complex parameters. In our previous paper (Mathematical Methods in the Applied Sciences 2001; 24(15) : 1139,1169), we have derived the asymptotic approximations for the eigenvalues and eigenfunctions of the aforementioned non-selfadjoint operators when the boundary parameters were arbitrary complex numbers except for one specific value of one of the parameters. We call this value the critical value of the boundary parameter. It has been shown (in Mathematical Methods in the Applied Sciences 2001; 24(15) : 1139,1169) that the entire set of the eigenvalues is located in a strip parallel to the real axis. The latter property is crucial for the proof of the fact that the set of the root vectors of the operator forms a Riesz basis in the state space of the system. In the present paper, we derive the asymptotics of the spectrum exactly in the case of the critical value of the boundary parameter. We show that in this case, the asymptotics of the eigenvalues is totally different, i.e. both the imaginary and real parts of eigenvalues tend to ,as the number of an eigenvalue increases. We will show in our next paper, that as an indirect consequence of such a behaviour of the eigenvalues, the set of the root vectors of the corresponding operator is not uniformly minimal (let alone the Riesz basis property). Copyright © 2003 John Wiley & Sons, Ltd. [source] The mapping properties of the radiosity operator along an edgeMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2002Olaf Hansen Abstract In this article we study the radiosity operator along an edge between two adjacent half-planes. First we show that the radiosity operator is invertible in a whole scale of anisotropic Sobolev spaces. In the absence of any shadows we are able to derive regularity properties of the solution, which depend only on the angle between the half-planes, the reflectivity coefficients and the right-hand side. This work can be considered as a supplement to the article of Rathsfeld (Mathematical Methods in the Applied Sciences 1999; 22: 217,241). Copyright © 2002 John Wiley & Sons, Ltd. [source] Three-Dimensional Surface Texture Characterization of Portland Cement Concrete PavementsCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 3 2007Ala Abbas Ten PCC field cores of varying surface textures were included in the analysis. X-ray Computed Tomography (CT) was used to scan the upper portion of these cores, resulting in a stack of two-dimensional grayscale images. Image processing techniques were utilized to isolate the void pixels from the solid pixels and reconstruct the three-dimensional surface topography. The resulting three-dimensional surfaces were reduced to two-dimensional "map of heights" images, whereby the grayscale intensity of each pixel within the image represented the vertical location of the surface at that point with respect to the lowest point on the surface. The "map of heights" images were analyzed using four mathematical methods, namely the Hessian model, the Fast Fourier transform (FFT), the wavelet analysis, and the power spectral density (PSD). Results obtained using these methods were compared to the mean profile depth (MPD) computed in accordance with ASTM E1845. [source] Methods to Determine Storativity of Infinite Confined Aquifers from a Recovery TestGROUND WATER, Issue 4 2002Djaouida Chenaf Starting from the equations of Theis and Cooper-Jacob, two new mathematical methods are proposed for interpreting the residual drawdown data for an infinite confined aquifer. Under Theis' assumptions and using the Cooper-Jacob approximation, the principal aquifer characteristics of transmissivity, pumping storativity, and recovery storativity are expressed without any correction or additional assumption. An actual case is used for illustration and confirms the validity of proposed equations and methods. [source] Special issue on recent advances in computational techniques for biomedical imaging,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2009Guo-Wei Wei Guest Editor Abstract A total of 12 papers in the area of mathematical methods and computational techniques for biomedical imaging and image analysis are presented in this special issue. Copyright © 2009 John Wiley & Sons, Ltd. [source] A comparison of modern data analysis methods for X-ray and neutron specular reflectivity dataJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 5 2007A. Van Der Lee Data analysis methods for specular X-ray or neutron reflectivity are compared. The methods that have been developed over the years can be classified into different types. The so-called classical methods are based on Parrat's or Abelès' formalism and rely on minimization using more or less evolved Levenberg,Marquardt or simplex routines. A second class uses the same formalism, but optimization is carried out using simulated annealing or genetic algorithms. A third class uses alternative expressions for the reflectivity, such as the Born approximation or distorted Born approximation. This makes it easier to invert the specular data directly, coupled or not with classical least-squares or iterative methods using over-relaxation or charge-flipping techniques. A fourth class uses mathematical methods founded in scattering theory to determine the phase of the scattered waves, but has to be coupled in certain cases with (magnetic) reference layers. The strengths and weaknesses of a number of these methods are evaluated using simulated and experimental data. It is shown that genetic algorithms are by far superior to traditional and advanced least-squares methods, but that they fail when the layers are less well defined. In the latter case, the methods from the third or fourth class are the better choice, because they permit at least a first estimate of the density profile to be obtained that can be refined using the classical methods of the first class. It is also shown that different analysis programs may calculate different reflectivities for a similar chemical system. One reason for this is that the representation of the layers is either described by chemical composition or by scattering length or electronic densities, between which the conversion of the absorptive part is not straightforward. A second important reason is that routines that describe the convolution with the instrumental resolution function are not identical. [source] Basics and applications of solid-state kinetics: A pharmaceutical perspective,JOURNAL OF PHARMACEUTICAL SCIENCES, Issue 3 2006Ammar Khawam Abstract Most solid-state kinetic principles were derived from those for homogenous phases in the past century. Rate laws describing solid-state degradation are more complex than those in homogenous phases. Solid-state kinetic reactions can be mechanistically classified as nucleation, geometrical contraction, diffusion, and reaction order models. Experimentally, solid-state kinetics is studied either isothermally or nonisothermally. Many mathematical methods have been developed to interpret experimental data for both heating protocols. These methods generally fall into one of two categories: model-fitting and model-free. Controversies have arisen with regard to interpreting solid-state kinetic results, which include variable activation energy, calculation methods, and kinetic compensation effects. Solid-state kinetic studies have appeared in the pharmaceutical literature over many years; some of the more recent ones are discussed in this review. © 2006 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 95:472,498, 2006 [source] Fluorescence and Raman spectra on painting materials: reconstruction of spectra with mathematical methodsJOURNAL OF RAMAN SPECTROSCOPY, Issue 10 2006Iacopo Osticioli Abstract SERDS (shift excitation difference spectroscopy) and SSRS (subtracted shifted Raman spectroscopy) methods were applied for fluorescence-background rejection in the Raman spectra of colored materials. These techniques are based on the assumption that the fluorescence contribution can be completely eliminated by subtracting two Raman spectra acquired at two shifted laser excitation frequencies. For the SERDS method a micro-Raman experimental apparatus coupled with a tunable diode laser (central emission at 684 nm) was set up. SSRS measurements were made on a commercial micro-Raman instrument; in this case the shifted spectrum was obtained by moving the spectrometer grating. Raman spectra were then reconstructed by applying the difference deconvolution method that automatically converts the difference signals in Raman peaks through a deconvolution operation. These techniques were tested on two reference colors (ultramarine and 6,6,-dibromoindigotine) and two colored samples of unknown composition (a Pompeian pink powder and a blue paint from a XVII century painting). Fluorescence-background subtraction and the following operation of spectra reconstruction took place successfully with no errors in Raman peaks, width and wavenumber position. In addition, even weak spectral details were revealed favoring the comparison with reference data for a molecular identification. Copyright © 2006 John Wiley & Sons, Ltd. [source] Alveolar and bronchial nitric oxide output in healthy childrenPEDIATRIC PULMONOLOGY, Issue 12 2008Anna Sepponen MD Abstract Exhaled nitric oxide (NO) concentration is a marker of pulmonary inflammation. It is usually measured at a single exhalation flow rate. However, measuring exhaled NO at multiple flow rates allows assessment of the flow-independent NO parameters: alveolar NO concentration, bronchial NO flux, bronchial wall NO concentration, and bronchial diffusing capacity of NO. Our aim was to determine the flow-independent NO parameters in healthy schoolchildren and to compare two different mathematical approaches. Exhaled NO was measured at four flow rates (10, 50, 100, and 200 ml/sec) in 253 schoolchildren (7,13 years old). Flow-independent NO parameters were calculated with linear method (flows ,50 ml/sec) and non-linear method (all flows). Sixty-six children (32 boys and 34 girls) with normal spirometry and no history or present symptoms of asthma, allergy, atopy or other diseases were included in the analysis. Median bronchial NO flux was 0.4 nl/sec (mean,±,SD: 0.5,±,0.3 nl/sec) and median alveolar NO concentration was 1.9 ppb (2.0,±,0.8 ppb) with the linear method. Bronchial NO flux correlated positively with height (r,=,0.423; P,<,0.001), FEV1 (r,=,0.358; P,=,0.003), and FVC (r,=,0.359; P,=,0.003). With the non-linear method, median bronchial wall NO concentration was 49.6 ppb (68.0,±,53.3 ppb) and bronchial diffusing capacity of NO was 10.0 pl/sec/ppb (11.8,±,7.5 pl/sec/ppb). The non-linear method gave lower alveolar NO concentration (1.4 [1.5,±,0.7] ppb, P,<,0.001) and higher bronchial NO flux (0.5 [0.6,±,0.3] nl/sec, P,<,0.001) than the linear method, but the results were highly correlated between the two methods (r,=,0.854 and r,=,0.971, P,<,0.001). In conclusion, the multiple flow rate method is feasible in children but different mathematical methods give slightly different results. Reference values in healthy children are of value when applying bronchial and alveolar NO parameters in the diagnostics and follow-up of inflammatory lung diseases. Pediatr. Pulmonol. 2008; 43:1242,1248. © 2008 Wiley-Liss, Inc. [source] | |||||||||||||