Numerical computation of an analytic singular value decomposition of a matrix valued function

This paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of factorizationsE(t)=X(t)S(t)Y(t) T whereX(t) andY(t) are orthogonal andS(t) is diagonal. To maintain differentiability the diagonal entries ofS(t) are allowed to be either positive or negative and to appear in any order. This paper investigates existence and uniqueness of analytic SVD's and develops an algorithm for computing them. We show that a real analytic pathE(t) always admits a real analytic SVD, a full-rank, smooth pathE(t) with distinct singular values admits a smooth SVD. We derive a differential equation for the left factor, develop Euler-like and extrapolated Euler-like numerical methods for approximating an analytic SVD and prove that the Euler-like method converges.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

Re-conceptualising IS function's support performance : a preliminary model

While IS function has gained widespread attention for over two decades, there is little consensus among information systems (IS) researchers and practitioners on how best to evaluate IS function's support performance. This paper reports on preliminary findings of a larger research effort proceeds from a central interest in the importance of evaluating IS function's support in organisations. This study is the first that attempts to re-conceptualise and conceive evaluate IS function's support as a multi- dimensional formative construct. We argue that a holistic measure for evaluating evaluate IS function's support should consist of dimensions that together assess the variety of the support functions and the quality of the support services provided to end-users. Thus, the proposed model consists of two halves, "Variety" and "Quality" within which resides seven dimensions. The Variety half includes five dimensions: Training; Documentation; Data- related Support, Software-related Support; and Hardware-related Support. The Quality half includes two dimensions: IS Support Staff and Support Services Performance. The proposed model is derived using a directed content analysis of 83 studies; from top IS outlets, employing the characteristics of the analytic theory and consistent with formative construct development procedures.

Lay theories of anorexia nervosa : a discourse analytic study

Previous studies on lay theories of anorexia nervosa have examined the 'accuracy' of lay knowledge, and the identification of factors by family and friends that would encourage early interventions. In contrast to these approaches, we examine lay theories of anorexia nervosa using a critical psychology perspective. We argue that the use of a discourse analysis methodology enables the examination of the construction of lay theories through dominant concepts and ideas. Ten semi-structured interviews with five women and five men aged between 15 and 25 years were carried out. Participants were asked questions about three main aspects of anorexia nervosa: aetiology, treatment and relationship to gender. Each interview was analysed in terms of the structure, function and variability of discourse. Three discourses: sociocultural, individual and femininity, are discussed in relation to the interview questions. We conclude that, in this study, lay theories of anorexia nervosa were structured through key discourses that maintained a separation between sociocultural aspects of anorexia nervosa and individual psychology. This separation exists in dominant psychomedical conceptualizations of anorexia nervosa, reinforcing the concept that it is a form of psychopathology.

“Lay” theories of anorexia nervosa : a discourse analytic study

Previous studies on lay theories of anorexia nervosa have examined the ‘accuracy’ of lay knowledge, and the identification of factors by family and friends that would encourage early interventions (Huon, Brown, & Morris, 1988, 7, 239–252; Murray, Touyz, & Beumont, 1990, 9, 87–93). In contrast to these approaches, we examine lay theories of anorexia nervosa using a critical psychology perspective. We argue that the use of a discourse analysis methodology enables the examination of the construction of lay theories through dominant concepts and ideas. Ten semi-structured interviews with five women and five men aged between 15 and 25 years were carried out. Participants were asked questions about three main aspects of anorexia nervosa: aetiology, treatment and relationship to gender. Each interview was analysed in terms of the structure, function and variability of discourse. Three discourses: sociocultural, individual and femininity, are discussed in relation to the interview questions. We conclude that, in this study, lay theories of anorexia nervosa were structured through key discourses that maintained a separation between sociocultural aspects of anorexia nervosa and individual psychology. This separation exists in dominant psychomedical conceptualizations of anorexia nervosa, reinforcing the concept that it is a form of psychopathology.

A kinematic analysis of the hand function

Background The evaluation of the hand function is an essential element within the clinical practice. The usual assessments are focus on the ability to perform activities of daily life. The inclusion of instruments to measure kinematic variables provides a new approach to the assessment. Inertial sensors adapted to the hand could be used as a complementary instrument to the traditional assessment. Material: clinimetric assessment (Upper Limb Functional Index, Quick Dash), antrophometric variables (eight and weight), dynamometry (palm preasure) was taken. Functional analysis was made with Acceleglove system for the right hand and computer system. The glove has six acceleration sensor, one on each finger and another one on the reverse palm. Method Analytic, transversal approach. Ten healthy subject made six task on evaluation table (tripod pinch, lateral pinch and tip pinch, extension grip, spherical grip and power grip). Each task was made and measure three times, the second one was analyze for the results section. A Matlab script was created for the analysis of each movement and detection phase based on module vector. Results The module acceleration vector offers useful information of the hand function. The data analysis obtained during the performance of functional gestures allows to identify five different phases within the movement, three static phase and tow dynamic, each module vector was allied to one task. Conclusion Module vector variables could be used for the analysis of the different task made by the hand. Inertial sensor could be use as a complement for the traditional assessment system.

Probabilistic multi-tensor estimation using the tensor distribution function

Diffusion weighted magnetic resonance (MR) imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of 6 directions, second-order tensors can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve crossing fiber tracts. Recently, a number of high-angular resolution schemes with greater than 6 gradient directions have been employed to address this issue. In this paper, we introduce the Tensor Distribution Function (TDF), a probability function defined on the space of symmetric positive definite matrices. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the diffusion orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function.

The tensor distribution function

Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.

Fast decay of the velocity autocorrelation function in dense shear flow of inelastic hard spheres

We find in complementary experiments and event-driven simulations of sheared inelastic hard spheres that the velocity autocorrelation function psi(t) decays much faster than t(-3/2) obtained for a fluid of elastic spheres at equilibrium. Particle displacements are measured in experiments inside a gravity-driven flow sheared by a rough wall. The average packing fraction obtained in the experiments is 0.59, and the packing fraction in the simulations is varied between 0.5 and 0.59. The motion is observed to be diffusive over long times except in experiments where there is layering of particles parallel to boundaries, and diffusion is inhibited between layers. Regardless, a rapid decay of psi(t) is observed, indicating that this is a feature of the sheared dissipative fluid, and is independent of the details of the relative particle arrangements. An important implication of our study is that the non-analytic contribution to the shear stress may not be present in a sheared inelastic fluid, leading to a wider range of applicability of kinetic theory approaches to dense granular matter.

Dynamic structure factor across the liquid-solid interface: appearance of a delta-function elastic peak

We present a theoretical calculation of the dynamic structure factor, S(k, ω), at the liquid-solid interface for large values of the wavevector k. An analytic expression is derived which shows the evolution of the elastic peak as the solid surface is approached from the liquid side.

Composition operators on vector-valued BMOA and related function spaces

A composition operator is a linear operator between spaces of analytic or harmonic functions on the unit disk, which precomposes a function with a fixed self-map of the disk. A fundamental problem is to relate properties of a composition operator to the function-theoretic properties of the self-map. During the recent decades these operators have been very actively studied in connection with various function spaces. The study of composition operators lies in the intersection of two central fields of mathematical analysis; function theory and operator theory. This thesis consists of four research articles and an overview. In the first three articles the weak compactness of composition operators is studied on certain vector-valued function spaces. A vector-valued function takes its values in some complex Banach space. In the first and third article sufficient conditions are given for a composition operator to be weakly compact on different versions of vector-valued BMOA spaces. In the second article characterizations are given for the weak compactness of a composition operator on harmonic Hardy spaces and spaces of Cauchy transforms, provided the functions take values in a reflexive Banach space. Composition operators are also considered on certain weak versions of the above function spaces. In addition, the relationship of different vector-valued function spaces is analyzed. In the fourth article weighted composition operators are studied on the scalar-valued BMOA space and its subspace VMOA. A weighted composition operator is obtained by first applying a composition operator and then a pointwise multiplier. A complete characterization is given for the boundedness and compactness of a weighted composition operator on BMOA and VMOA. Moreover, the essential norm of a weighted composition operator on VMOA is estimated. These results generalize many previously known results about composition operators and pointwise multipliers on these spaces.

Computation of the ambiguity function for circularly symmetric pupils

A method of computing the ambiguity function (AF) for a circularly symmetric pupil function is presented. The AFs of a clear aperture and two shaded apertures are considered in detail and an explicit expression for the first of these AFs is given. We explain these results in the context of the well-known optical transfer function theory and show a primary application of these computations. A good analytic approximation is also introduced, providing an alternative method for calculating the AF, in a simpler way.

Analytic expression of the diffraction of a circular aperture

Recurring to the characteristic of Bessel function, we give the analytic expression or the Fresnel diffraction by a circular aperture, thus the diffractions on the propagation axis and along the boundary of the geometrical shadow are discussed conveniently. Since it is difficult to embody intuitively the physical meaning from this series expression of the Fresnel diffraction, after weighing the diffractions on the axis and along the boundary of the geometrical shadow, we propose a simple approximate expression of the circular diffraction, which is equivalent to the rigorous solution in the further propagation distance. It is important for the measurement of the parameter or the beam, such as the quantitative analysis of the relationship of the wave error and the divergence of the beam, In this paper, the relationship of the fluctuation of the transverse diffraction profile and the position of the axial point is discussed too. (c) 2005 Elsevier GrnbH. All rights reserved.

Computing Zeros of Analytic Functions in the Complex Plane without using Derivatives

A new approach to evaluating all multiple complex roots of analytical function f(z) confined to the specified rectangular domain of complex plane has been developed and implemented in Fortran code. Generally f (z), despite being holomorphic function, does not have a closed analytical form thereby inhibiting explicit evaluation of its derivatives. The latter constraint poses a major challenge to implementation of the robust numerical algorithm. This work is at the instrumental level and provides an enabling tool for solving a broad class of eigenvalue problems and polynomial approximations.