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.

Detection and Characterization of Long-Pulse Low-Velocity Impact Damage in Plastic Bonded Explosives

Damage not only degrades the mechanical properties of explosives, but also influences the shock sensitivity, combustion and even detonation behavior of explosives. The study of impact damage is crucial in the vulnerability evaluation of explosives. A long-pulse low-velocity gas gun with a gas buffer was developed and used to induce impact damage in a hot pressed plastic bonded explosive. Various methods were used to detect and characterize the impact damage of the explosive. The microstructure was examined by use of polarized light microscopy. Fractal analysis of the micrographs was conducted by use of box counting method. The correlation between the fractal dimensions and microstructures was analyzed. Ultrasonic testing was conducted using a pulse through-transmission method to obtain the ultrasonic velocity and ultrasonic attenuation. Spectra analyses were carried out for recorded ultrasonic signals using fast Fourier transform. The correlations between the impact damage and ultrasonic parameters including ultrasonic velocities and attenuation coefficients were also analyzed. To quantitatively assess the impact induced explosive crystal fractures, particle size distribution analyses of explosive crystals were conducted by using a thorough etching technique, in which the explosives samples were soaked in a solution for enough time that the binder was totally removed. Impact induces a large extent of explosive crystal fractures and a large number of microcracks. The ultrasonic velocity decreases and attenuation coefficients increase with the presence of impact damage. Both ultrasonic parameters and fractal dimension can be used to quantitatively assess the impact damage of plastic bonded explosives.

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。

Analysis of the ellipsometric spectra of amorphous carbon thin films for evaluation of the sp3-bonded carbon content

Using spcctroscopic ellipsometry (SE), we have measured the optical properties and optical gaps of a series of amorphous carbon (a-C) films ∼ 100-300 Å thick, prepared using a filtered beam of C+ ions from a cathodic arc. Such films exhibit a wide range of sp3-bonded carbon contents from 20 to 76 at.%, as measured by electron energy loss spectroscopy (EELS). The Taue optical gaps of the a-C films increase monotonically from 0.65 eV for 20 at.% sp3 C to 2.25 eV for 76 at.% sp3 C. Spectra in the ellipsometric angles (1.5-5 eV) have been analyzed using different effective medium theories (EMTs) applying a simplified optical model for the dielectric function of a-C, assuming a composite material with sp2 C and sp3 C components. The most widely used EMT, namely that of Bruggeman (with three-dimensionally isotropic screening), yields atomic fractions of sp3 C that correlate monotonically with those obtained from EELS. The results of the SE analysis, however, range from 10 to 25 at.% higher than those from EELS. In fact, we have found that the volume percent sp3 C from SE using the Bruggeman EMT shows good numerical agreement with the atomic percent sp3 C from EELS. The SE-EELS discrepancy has been reduced by using an optical model in which the dielectric function of the a-C is determined as a volume-fraction-weighted average of the dielectric functions of the sp2 C and sp3 C components. © 1998 Elsevier Science S.A.

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.