Sign changes of Fourier coefficients of Hilbert modular forms

Sign changes of Fourier coefficients of various modular forms have been studied. In this paper, we analyze some sign change properties of Fourier coefficients of Hilbert modular forms, under the assumption that all the coefficients are real. The quantitative results on the number of sign changes in short intervals are also discussed. (C) 2014 Elsevier Inc. All rights reserved.

Molecular profiling of sepsis in mice using Fourier Transform Infrared Microspectroscopy

Sepsis is a life threatening condition resulting from a high burden of infection. It is a major health care problem and associated with inflammation, organ dysfunction and significant mortality. However, proper understanding and delineating the changes that occur during this complex condition remains a challenge. A comparative study involving intra-peritoneal injection of BALB/c mice with Salmonella Typhimurium (infection), lipopolysaccharide (endotoxic shock) or thioglycollate (sterile peritonitis) was performed. The changes in organs and sera were profiled using immunological assays and Fourier Transform Infrared (FTIR) micro-spectroscopy. There is a rapid rise in inflammatory cytokines accompanied with lowering of temperature, respiratory rate and glucose amounts in mice injected with S. Typhimurium or lipopolysaccharide. FTIR identifies distinct changes in liver and sera: decrease in glycogen and protein/lipid ratio and increase in DNA and cholesteryl esters. These changes were distinct from the pattern observed in mice treated with thioglycollate and the differences in the data obtained between the three models are discussed. The combination of FTIR spectroscopy and other biomarkers will be valuable in monitoring molecular changes during sepsis. GRAPHICS] Intra-peritoneal infection with high dose of Salmonella Typhimurium leads to rapid increase in inflammatory cytokines, e.g. Tnf alpha (A). FTIR analysis of liver (B) and sera (C) identifies several metabolic changes: glycogen, protein/lipid, cholesteryl esters and DNA.

On Fast Bilateral Filtering Using Fourier Kernels

It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the nonlinear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation have, however, been restricted to Gaussian range kernels. In this work, we propose a novel approximation that can be applied to any range kernel, provided it has a pointwise-convergent Fourier series. More specifically, we propose to approximate the Gaussian range kernel of the bilateral filter using a Fourier basis, where the coefficients of the basis are obtained by solving a series of least-squares problems. The coefficients can be efficiently computed using a recursive form of the QR decomposition. By controlling the cardinality of the Fourier basis, we can obtain a good tradeoff between the run-time and the filtering accuracy. In particular, we are able to guarantee subpixel accuracy for the overall filtering, which is not provided by the most existing methods for fast bilateral filtering. We present simulation results to demonstrate the speed and accuracy of the proposed algorithm.

Cuspidality and the growth of Fourier coefficients of modular forms : A survey

In this paper, we present a survey of the recent results on the characterization of the cuspidality of classical modular forms on various groups by a suitable growth of their Fourier coefficients.

A NOTE ON SMALL GAPS BETWEEN NONZERO FOURIER COEFFICIENTS OF CUSP FORMS

It is shown that there are infinitely many primitive cusp forms f of weight 2 with the property that for all X large enough, every interval (X, X + cX(1/4)), where c > 0 depends only on the form, contains an integer n such that the n-th Fourier coefficient of f is nonzero.

Fourier Transform Method for Measuring the Micro Amplitu of Water Surface Waves

采用一种非接触的光学方法傅立叶变换莫尔法(Fourier transform method),结合数字图像处理技术,对微幅振荡的水表面波的振幅进行测量.它是对全场中每一个像素点进行测量,比接触测量法具有更高的灵敏度.它为微幅水表面波振幅的测量提供了一种手段.通过将计算机生成的周期性光栅图像经投影机直接投影到被测物体的参考平面,经CCD摄像头、图像板捕捉存储形成数字化的光栅图像,利用傅立叶变换莫尔法处理光栅图像,从而获得包含有水表面波的振幅的相位信息,再经适当的几何变换获得振幅信息.我们在垂直振荡装置上进行了不同激励频率和不同振幅的表面波的振幅测量.

一种快速逼近Fourier级数和实用算子

采用逐次平均方法，构造一种快速逼近Ｆｏｕｒｉｅｒ级数和实用算子（逐次平均算子），用这种算子来取代Ｆｏｕｒｉｅｒ级数无穷项求和，具有误差小，收敛速度快的功能。志Ｆｅｊｅｒ算子比，它的逼近性要好得多，与Ｋｏｒｂｉｎ算子比，它更易于实用，理论证明其一般性，计算著名的Ｓａｆｆｍａｎ－Ｔａｙｌｏｒ粘性指进问题时应用逐次平均算子，既不产生大的截断误差，又能避免高频振荡而使计算过程稳定，得到很好的结果。

Aplicación de parámetros matemáticos en un trabajo multidisciplinario de composición musical asistida por computadora sobre una temática folklórica

Resumen: En el marco de un proyecto de la Vicerrectoría de Investigaciones de la Universidad de Caldas denominado “Resignificación músico-pictórica del mito de la Salamanca” surgió la conveniencia de aplicar y diseñar programas de fundamentación matemática que permitieran definir la estructura y el tratamiento acústico de la obra especialmente escrita para este proyecto. Principalmente nos basamos en la implementación de la Transformada Rápida de Fourier (Fast Fourier Transform) para el análisis de espectros armónicos y su modificación en vivo y en la utilización de un entorno de programación para procesamiento de sonido en tiempo real. El marco general de la investigación parte del enfoque de Regionalismo Crítico procedente de las propuestas de Kenneth Frampton referentes originalmente a la crítica de la arquitectura. El planteamiento como investigación mutidisciplinaria implica (1) una visión crítica de la substancia mítica y social subyacente, (2) una resignificación pictórica por medio de fotografía, animación y pintura, basada en la sustancia visual que contiene el mito, (3) un enfoque musical electroacústico, a partir del material que surge del folklor local, utilizando la intervención de instrumentos en vivo y procesamiento en tiempo real.

Compact finite difference - Fourier spectral method for three-dimensional incompressible Navier-Stokes equations

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.