Search results for "Fourier Analysis"
showing 10 items of 113 documents
Improved Bounds for Hermite–Hadamard Inequalities in Higher Dimensions
2019
Let $\Omega \subset \mathbb{R}^n$ be a convex domain and let $f:\Omega \rightarrow \mathbb{R}$ be a positive, subharmonic function (i.e. $\Delta f \geq 0$). Then $$ \frac{1}{|\Omega|} \int_{\Omega}{f dx} \leq \frac{c_n}{ |\partial \Omega| } \int_{\partial \Omega}{ f d\sigma},$$ where $c_n \leq 2n^{3/2}$. This inequality was previously only known for convex functions with a much larger constant. We also show that the optimal constant satisfies $c_n \geq n-1$. As a byproduct, we establish a sharp geometric inequality for two convex domains where one contains the other $ \Omega_2 \subset \Omega_1 \subset \mathbb{R}^n$: $$ \frac{|\partial \Omega_1|}{|\Omega_1|} \frac{| \Omega_2|}{|\partial \Ome…
Multipliers on Vector Valued Bergman Spaces
2002
AbstractLet X be a complex Banach space and let Bp(X) denote the vector-valued Bergman space on the unit disc for 1 ≤ p < ∞. A sequence (Tn)n of bounded operators between two Banach spaces X and Y defines a multiplier between Bp(X) and Bq(Y) (resp. Bp(X) and lq(Y)) if for any function we have that belongs to Bq(Y) (resp. (Tn(xn))n ∈ lq(Y)). Several results on these multipliers are obtained, some of them depending upon the Fourier or Rademacher type of the spaces X and Y. New properties defined by the vector-valued version of certain inequalities for Taylor coefficients of functions in Bp(X) are introduced.
ATR-FTIR spectroscopy as a quality control system for monitoring the storage of blood products
2021
Blood screening is a fundamental part of disease diagnosis and monitoring health. Attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy offers an innovative solution to streamlining the process, especially for multianalyte detection in aqueous samples. However, samples always undergo a storage phase before they are processed for testing and blood transfusion. In this study, we investigated the effect of standard storage procedures on the macromolecular composition of whole blood, and plasma collected in blood tubes for diagnostic purposes and initial screening of blood products. Periphery blood samples were collected from 10 volunteers and then stored for 14 days a…
Representation of solutions and large-time behavior for fully nonlocal diffusion equations
2017
Abstract We study the Cauchy problem for a nonlocal heat equation, which is of fractional order both in space and time. We prove four main theorems: (i) a representation formula for classical solutions, (ii) a quantitative decay rate at which the solution tends to the fundamental solution, (iii) optimal L 2 -decay of mild solutions in all dimensions, (iv) L 2 -decay of weak solutions via energy methods. The first result relies on a delicate analysis of the definition of classical solutions. After proving the representation formula we carefully analyze the integral representation to obtain the quantitative decay rates of (ii). Next we use Fourier analysis techniques to obtain the optimal dec…
Silhouette encoding and synthesis using elliptic Fourier descriptors and applications to videoconferencing, Journal of Visual Language and Computing
2004
This paper investigates the use of elliptic Fourier descriptors as a shape descriptor for encoding the silhouette of a person. Shape descriptors are here used for predicting the shape of silhouettes in missing frames within a sequence. This prediction scheme is applied to the case of generating in-between images in a low frame rate videoconferencing system, where the reconstructed silhouette is used as a binary mask for reducing the computational time for the frame reconstruction.
Photonic fractional Fourier transformer with a single dispersive device
2013
In this work we used the temporal analog of spatial Fresnel diffraction to design a temporal fractional Fourier transformer with a single dispersive device, in this way avoiding the use of quadratic phase modulators. We demonstrate that a single dispersive passive device inherently provides the fractional Fourier transform of an incident optical pulse. The relationships linking the fractional Fourier transform order and scaling factor with the dispersion parameters are derived. We first provide some numerical results in order to prove the validity of our proposal, using a fiber Bragg grating as the dispersive device. Next, we experimentally demonstrate the feasibility of this proposal by us…
Phase error analysis of clipped waveforms in surface topography measurement using projected fringes
2021
Abstract When working with the method of projected fringes outside the optical laboratory one often encounters the problem of uncontrollable ambient light. This might cause saturation of the camera which in turn results in clipping of the fringes. Since standard theories describing phase-shifting techniques assume the projected fringes to be purely sinusoidal, such clipping will result in measurement error. In this paper a detailed analysis of this problem is given, and relations between phase errors, the amount of fringe clipping and the number of phase steps are found. Moreover, the phase difference between the clipped and the unclipped fringes is described. This investigation is based on…
Cross-diffusion-induced subharmonic spatial resonances in a predator-prey system.
2018
In this paper we investigate the complex dynamics originated by a cross-diffusion-induced subharmonic destabilization of the fundamental subcritical Turing mode in a predator-prey reaction-diffusion system. The model we consider consists of a two-species Lotka-Volterra system with linear diffusion and a nonlinear cross-diffusion term in the predator equation. The taxis term in the search strategy of the predator is responsible for the onset of complex dynamics. In fact, our model does not exhibit any Hopf or wave instability, and on the basis of the linear analysis one should only expect stationary patterns; nevertheless, the presence of the nonlinear cross-diffusion term is able to induce …
Hadamard NMR imaging with slice selection
1996
Stochastic NMR imaging is one of the less common NMR imaging techniques. Nevertheless, stochastic rf excitation is characterized by some remarkable features: the rf excitation power is at least two orders of magnitude lower in comparison to conventionally pulsed NMR imaging schemes. Thus, the technique is of interest for imaging of large objects. The systematic noise inherent in images obtained with random noise excitation has been eliminated by using pseudorandom noise together with Hadamard transformation for data evaluation. Data acquisition times are comparable to those of ultrafast imaging techniques. For slice selection, z magnetization is destroyed outside the slice region with speci…
Use of middle cerebral velocity and blood pressure for the analysis of cerebral autoregulation at various frequencies: The coherence index
1998
A common component in many protocols for the evaluation of cerebral autoregulation is the comparison of transcranial Doppler ultrasound (TCD) velocities with blood pressure recordings, in which correlations between these two signals correspond to impaired autoregulation. With long data sets and complicated paradigms, however, visual inspection alone cannot adequately distinguish random coincidence from consistent correlation in a statistically valid fashion. We suggest and illustrate the use of the coherence index for this purpose. To illustrate this technique, long-term recordings of TCD velocity and blood pressure were obtained from 6 normal subjects and using 23 data segments from 8 pati…