Search results for "Fourier Analysis"
showing 10 items of 113 documents
Convolution of three functions by means of bilinear maps and applications
1999
When dealing with spaces of vector-valued analytic functions there is a natural way to understand multipliers between them. If X and Y are Banach spaces and L(X,Y ) stands for the space of linear and continuous operators we may consider the convolution of L(X,Y )-valued analytic functions, say F (z) = ∑ n=0∞ Tnz , and X-valued polynomials, say f(z) = ∑m n=0 xnz , to get the Y -valued function F ∗ f(z) = ∑ Tn(xn)z. The second author considered such a definition and studied multipliers between H(X) and BMOA(Y ) in [5]. When the functions take values in a Banach algebra A then the natural extension of multiplier is simply that if f(z) = ∑ anz n and g(z) = ∑ bnz , then f ∗ g(z) = ∑ an.bnz n whe…
Performance analysis of optical imaging systems based on the fractional fourier transform
1998
Some image quality parameters, such as the Strehl ratio and the optical transfer function, are analysed in the generalized phase-space, or x-p domain, of the fractional Fourier transform associated with a modified one-dimensional pupil function. Some experimental results together with computer simulations are performed which illustrate the tolerance to defocus of different apertures.
Incorporation and metabolism of trans 20∶5 in endothelial cells. Effect on prostacyclin synthesis
2000
To study the ability of long-chain trans fatty acids (FA) to be incorporated and metabolized into endothelial cells, bovine aortic endothelial cells were incubated with medium enriched eicosapentaenoic acid (EPA) bound to albumin (M2) or one of its geometrical isomers: 20:5 5c,8c,11t,14c,17c (M3), 20:5 5c,8c,11c,14c,17t (M4), or 20:5 5c,8c,11t,14c,17t (M5). After 48 h of incubation, supernatant and cells were harvested and their lipids were analyzed, including prostacyclin synthesis. EPA and 22:5n-3 of endothelial cells incubated with M2 were, respectively, three and two times higher than in control cells (incubated in M1, without any fatty acid added), whereas 22:6n-3 increased only in the…
Automatic Recognition and Analysis of Scanned Non-crimp Fabrics for Calculation of their Fluid Flow Permeability
2007
Automatic recognition of scanned images of distorted bi-axial fiber bundle arrangements is considered in order to obtain the overall permeability of the formed fiber network. Scanned images are pre-processed with color normalization followed by usage of a threshold to find the pixels belonging to the bundles, the threads keeping the bundles together, and the distinct gaps formed between the bundles. Since the scanned images virtually have a perfect grayscale, the intensity can be treated as a corresponding signal of the image. Next the regular character of the fiber network is investigated using Fourier analysis on the fiber bundles as well as on the threads. The direction, position, and s…
Dynamic shakedown of structures under repeated seismic loads
1995
Elastic, perfectly plastic structures are considered under the action of repeated short-duration exitations of seismic type acting in an unknown time sequence, but belonging to a given polyhedral excitation domain. The basic excitations (vertices of the polyhedron) are chosen as discrete-spectrum waves each with frequencies coincident with the first natural frequencies of the structure, and amplitudes related to the ground features and earthquake intensity (according to the Kanai and Tajimi filter model) in such a way that every admissible excitation-obtained as a linear convex combination of the basic ones-has a maximum power not exceeding a given value. In the framework of unrestricted dy…
Universal natural shapes: From unifying shape description to simple methods for shape analysis and boundary value problems
2012
Gielis curves and surfaces can describe a wide range of natural shapes and they have been used in various studies in biology and physics as descriptive tool. This has stimulated the generalization of widely used computational methods. Here we show that proper normalization of the Levenberg-Marquardt algorithm allows for efficient and robust reconstruction of Gielis curves, including self-intersecting and asymmetric curves, without increasing the overall complexity of the algorithm. Then, we show how complex curves of k-type can be constructed and how solutions to the Dirichlet problem for the Laplace equation on these complex domains can be derived using a semi-Fourier method. In all three …
Applications of sinusoidal phase modulation in temporal optics to highlight some properties of the Fourier transform
2019
International audience; Fourier analysis plays a major role in the analysis and understanding of many phenomena in physics and contemporary engineering. However, students, who have often discovered this notion through numerical tools, do not necessarily understand all the richness that can be derived from joint analysis in the temporal and spectral domains, particularly in the field of optics. As part of the second year of the Master's degree in Physics Lasers and Materials at the University of Burgundy, we have set up a set of experiments to highlight these concepts and to show, on a non-trivial example of periodic phase modulation, the precautions to be taken in the interpretation of the …
k-Space filtering in 2D gradient-echo breath-hold hyperpolarized3He MRI: Spatial resolution and signal-to-noise ratio considerations
2002
In this work some of the factors that can influence the signal-to-noise ratio (SNR) and spatial resolution in MR images of inhaled hyperpolarized gases are systematically addressed. In particular, the effects of RF depletion of longitudinal polarization and image gradient diffusion dephasing were assessed in terms of their contribution to a k-space filter. By means of theoretical simulations and a novel method of experimental validation using a variable transverse magnetization of the 1H signal, systematic quantitative and qualitative investigations of the effects of k-space filtering intrinsic to imaging of hyperpolarized gas were made. A 2D gradient-echo image is considered for a range of…
F-singularities via alterations
2011
For a normal F-finite variety $X$ and a boundary divisor $\Delta$ we give a uniform description of an ideal which in characteristic zero yields the multiplier ideal, and in positive characteristic the test ideal of the pair $(X,\Delta)$. Our description is in terms of regular alterations over $X$, and one consequence of it is a common characterization of rational singularities (in characteristic zero) and F-rational singularities (in characteristic $p$) by the surjectivity of the trace map $\pi_* \omega_Y \to \omega_X$ for every such alteration $\pi \: Y \to X$. Furthermore, building on work of B. Bhatt, we establish up-to-finite-map versions of Grauert-Riemenscheneider and Nadel/Kawamata-V…
Kurzweil-Henstock type integral in fourier analysis on compact zero-dimensional group
2009
Abstract A Kurzweil-Henstock type integral defined on a zero-dimensional compact abelian group is studied and used to obtain a generalization of some results related to the problem of recovering, by generalized Fourier formulae, the coefficients of convergent series with respect to the characters of such a group.