On boundary value problems for the domain exterior to a thin or slender region

In this paper a method for obtaining uniformly valid asymptotic expansions of the solution of the boundary value problems in domains exterior to thin or slender regions is given. This approach combines the Tuck's method, based on the use of a suitable co-ordinates system with the method given by Handelsman and Keller yielding complete uniform asymptotic expansion of the solution for slender body problems. Our method avoids the determination of the extremities of the segment containing singularities; it is pointed out that this last problem is a pure geometrical one and independent of solving concrete boundary value problems in the given domain.     

Geodesic active contour under geometrical conditions: theory and 3D applications

In this paper, we propose a new scheme for both detection of boundaries and fitting of geometrical data based on a geometrical partial differential equation, which allows a rigorous mathematical analysis. The model is a geodesic-active-contour-based model, in which we are trying to determine a curve that best approaches the given geometrical conditions (for instance a set of points or curves to approach) while detecting the object under consideration. Formal results concerning existence, uniqueness (viscosity solution) and stability are presented as well. We give the discretization of the method using an additive operator splitting scheme which is very efficient for this kind of problem. We also give 2D and 3D numerical examples on real data sets.     

Extension of the scaled boundary finite element method to geometrical and physical nonlinearity

The scaled boundary finite element method (SBFEM) has been used in many fields of engineering to solve the governing equations in bounded and unbounded 2D as well as 3D domains. In solid mechanics, the semi-analytical solution strategy of the SBFE formulation (numerical in circumferential direction, analytical in radial direction) is based on the assumption of linear elastic material behavior and only small geometrical changes. However, a large group of materials (e.g. rubber) shows geometrical and physical nonlinearity at mechanical loading. In this contribution, the extension of the SBFEM to geometrical and physical nonlinearity is examined. A plane finite element is developed which uses the concept of shape functions constructed by the SBFEM in the framework of a nonlinear finite element analysis. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Aeroelastic analysis of large horizontal wind turbine baldes?

A nonlinear aeroelastic analysis method for large horizontal wind turbines is described. A vortex wake method and a nonlinear ?nite element method (FEM) are coupled in the approach. The vortex wake method is used to predict wind turbine aero-dynamic loads of a wind turbine, and a three-dimensional (3D) shell model is built for the rotor. Average aerodynamic forces along the azimuth are applied to the structural model, and the nonlinear static aeroelastic behaviors are computed. The wind rotor modes are obtained at the static aeroelastic status by linearizing the coupled equations. The static aeroelastic performance and dynamic aeroelastic responses are calculated for the NH1500 wind turbine. The results show that structural geometrical nonlinearities signi?cantly reduce displacements and vibration amplitudes of the wind turbine blades. Therefore, structural geometrical nonlinearities cannot be neglected both in the static aeroelastic analysis and dynamic aeroelastic analysis.     

Skew ray tracing and sensitivity analysis of ellipsoidal optical boundary surfaces

The 4 × 4 homogeneous transformation matrix is one of the most commonly applied mathematical tools in the fields of robotics, mechanisms and computer graphics. Here we extend further this mathematical tool to geometrical optics by addressing the following two topics: (1) skew ray tracing to determine the paths of reflected/refracted skew rays crossing ellipsoidal boundary surfaces; and (2) sensitivity analysis to determine via direct mathematical analysis the differential changes of the incident point and the reflected/refracted vector with respect to changes in the incident light source. The proposed ray tracing and sensitivity analysis are projected as the nucleus of other geometrical optical computations.     

Analysis of a family of discontinuous Galerkin methods for elliptic problems: the one dimensional case

Summary. In this paper we analyze a family of discontinuous Galerkin methods, parameterized by two real parameters, for elliptic problems in one dimension. Our main results are: (1) a complete inf-sup stability analysis characterizing the parameter values yielding a stable scheme and energy norm error estimates as a direct consequence thereof, (2) an analysis of the error in L² where the standard duality argument only works for special parameter values yielding a symmetric bilinear form and different orders of convergence are obtained for odd and even order polynomials in the nonsymmetric case. The analysis is consistent with numerical results and similar behavior is observed in two dimensions.Mathematics Subject Classification (2000): 65M60, 65M15Research supported by: The Swedish Foundation for International Cooperation in Research and Higher Education     

Auto-associative models and generalized principal component analysis

In this paper, we propose auto-associative (AA) models to generalize Principal component analysis (PCA). AA models have been introduced in data analysis from a geometrical point of view. They are based on the approximation of the observations scatter-plot by a differentiable manifold. In this paper, they are interpreted as Projection pursuit models adapted to the auto-associative case. Their theoretical properties are established and are shown to extend the PCA ones. An iterative algorithm of construction is proposed and its principle is illustrated both on simulated and real data from image analysis.     

Análise elastoplástica de estruturas aporticadas com superfícies de interação obtidas por regressão linear múltipla

The ultimate limit state criteria (yielding surfaces) applied to structural designs are easier in stress resultants. There are many difficulties to generating interaction surfaces with six sectional efforts obtained through to numerical or experimental models of a space-frame analysis. The approach, in the literature, to nonlinear analysis of structures with 3D beams is use of interaction surfaces with only three combined efforts in the cross-section. Therefore, a better understanding of load types, of interactions between the six efforts and of local and global stability of structure are necessary. The interaction surfaces with three efforts are presented in planes, quadrics, more complex, or a mixture of them shapes, so that techniques which use analytical formulations with combined efforts and several section shapes are more or less complex. Multiple linear regression allows to treat the resultant efforts of several analyses for obtaining a yielding surface with the combined efforts. In this paper, the formulation to obtaining of the surfaces and their applications in the analysis of elasto-plastic frame structures are presented.     

Interest point detection in images using complex network analysis

This paper presents a new application of complex network theory and tools to digital image analysis and computer vision problems in order to detect interest points in digital images. We associate a weighted geometrical and fast computable complex network to each image and then we propose two different methods to locate these feature points based on both local and global (spectral) centrality measures of the corresponding network.     

Fast algorithm for geometrical coding of digital images

A fast algorithm for geometrical coding is presented in the paper. It allows one to perform the image analysis by methods of differential geometry rather than widespread methods based on gradient and Hessian calculations. Nowadays, one of the most important aspects in image analysis is the speed of computations. The algorithm for geometrical coding is comparable or faster than traditional algorithms of image analysis and in many cases it gives better results. Several examples of algorithm working results for contour detection are presented.     

Self-adjoint Extensions for the Neumann Laplacian and Applications

A new technique is proposed for the analysis of shape optimization problems. The technique uses the asymptotic analysis of boundary value problems in singularly perturbed geometrical domains. The asymptotics of solutions are derived in the framework of compound and matched asymptotics expansions. The analysis involves the so-called interior topology variations. The asymptotic expansions are derived for a model problem, however the technique applies to general elliptic boundary value problems. The self-adjoint extensions of elliptic operators and the weighted spaces with detached asymptotics are exploited for the modelling of problems with small defects in geometrical domains, The error estimates for proposed approximations of shape functionals are provided.     

Isovecteurs pour l'équation de Hamilton–Jacobi–Bellman,différentielles stochastiques formelles et intégrales premières en mécanique quantique euclidienneIsovectors for the Hamilton–Jacobi–Bellman equation,formal stochastic differentials and constants of motion in Euclidean Quantum Mechanics

We give a stochastic interpretation of the geometrical representation, from E. Cartan, of the heat equation, in terms of ideal exterior differential forms and isovectors generating the symmetries of this equation. The method can also be used to interpret as a stochastic deformation the contact geometry of first order ordinary differential equations and the search for infinitesimal symmetries of the associated Hamilton–Jacobi equation. We thus generalise, in an elegant and geometrical way, the results coming originally from long calculations of stochastic analysis. To cite this article: P. Lescot, J.-C. Zambrini, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 263–266.     

Holomorphic horospherical duality “sphere-cone”

We describe a construction of complex geometrical analysis which corresponds to the classical theory of spherical harmonics.     

Computational considerations in functional principal component analysis

Computing estimates in functional principal component analysis (FPCA) from discrete data is usually based on the approximation of sample curves in terms of a basis (splines, wavelets, trigonometric functions, etc.) and a geometrical structure in the data space (L ² spaces, Sobolev spaces, etc.). Until now, the computational efforts have been focused in developing ad hoc algorithms to approximate those estimates by previously selecting an efficient approximating technique and a convenient geometrical structure. The main goal of this paper consists of establishing a procedure to formulate the algorithm for computing estimates of FPCA under general settings. The resulting algorithm is based on the classic multivariate PCA of a certain random vector and can thus be implemented in the majority of statistical packages. In fact, it is derived from the analysis of the effects of modifying the norm in the space of coordinates. Finally, an application on real data will be developed to illustrate the so derived theoretic results. This research has been supported by Project MTM2004-5992 from Dirección General de Investigación, Ministerio de Ciencia y Tecnología.     

Tauber-Bedingungen für Verfahren Mit Abschnittskonvergenz

We consider a summability matrix A with sectional convergence (in the null-domain) and use sectional submethods B. If (I - B)s has small oscillation (for a suitable B), then s also has small oscillation. Employing a set of such B, we obtain Tauberian results yielding convergence (also with one-sided conditions). In particular this analysis applies to weighted means. Thus we have a new approach to results given by Móricz and Rhoades [3].     

Credit scoring with macroeconomic variables using survival analysis

Survival analysis can be applied to build models for time to default on debt. In this paper, we report an application of survival analysis to model default on a large data set of credit card accounts. We explore the hypothesis that probability of default (PD) is affected by general conditions in the economy over time. These macroeconomic variables (MVs) cannot readily be included in logistic regression models. However, survival analysis provides a framework for their inclusion as time-varying covariates. Various MVs, such as interest rate and unemployment rate, are included in the analysis. We show that inclusion of these indicators improves model fit and affects PD yielding a modest improvement in predictions of default on an independent test set.     

塑性极限分析的不可微模型及其光滑化算法

藉助于凸规划的Lagrange对偶理论,建立了Mises屈服条件下理想刚塑性材料Hill最大塑性功原理的对偶问题,并据此建立了极限分析的一个不可微凸规划模型．该模型不仅避免了对屈服条件的线性化,而且其离散化形式为线性约束下Euclid模之和的极小化问题．针对Euclid模的不可微性,提出理想刚塑性体极限分析的一种光滑化算法．通过计算平面应力和平面应变问题的极限荷载因子和相应的坍塌机构,验证了算法的有效性．     

The horospherical duality

We discuss the horospherical duality as a geometrical background of harmonic analysis on semisimple symmetric spaces.     

Ordering Cellular Spaces with Application to Curves and Knots

This paper concerns the problem of ordering geometrical objects, which have the structure of finite cellular spaces. We introduce cellular codes, cellular indices, and (k,l)-sizes and apply them to ordering 2-cells, plane curves, and projections of knots. Results of this paper can be applied (1) to ordering other geometrical objects with cellular space structures, (2) in psychological and computer tests for comparison of complexity of geometrical objects, and (3) to ordering objects with fractal and chaotic structure, which admit approximation by cellular spaces.