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。

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.

用Fourier变换莫尔法测量流体自由表面微幅波的振幅

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。我们在生趣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。

Comparison of Experimental Strategies to Control Torpedograss

Studies were conducted to evaluate whether the herbicide imazapyr or a combination of imazapyr and fluridone could be used effectively to control torpedograss ( Panicum repens L.), an exotic perennial plant that has replaced more than 6,000 ha of native vegetation and degraded quality wildlife habitat in Lake Okeechobee, Florida. Torpedograss was controlled for more than one year in some areas following a single aerial treatment using 0.56, 0.84, or 1.12 kg acid equivalents (ae) imazapyr/ha. Combining imazapyr and fluridone did not increase the level of torpedograss control. In areas where plant biomass was reduced by fire prior to being treated with 0.84 or 1.12 kg ae imazapyr/ha, torpedograss was controlled for more than two years and native plant species, including duck potato ( Sagittaria lancifolia L.) and pickerelweed ( Pontederia cordata L.) became the dominant vegetation in less than one year. Although torpedograss was controlled in some areas, little or no long-term control was observed at 16 of the 26 treatment locations. To reduce the uncertainty associated with predicting long-term treatment affects, additional studies are needed to determine whether environmental factors such as periphyton mats, plant thatch, hydroperiod and water depth affect treatment efficacy. , he

Collecção das Leis do Imperio do Brasil de 1837

Parte 1 - Leis

Charles M. Breder, Jr.: Palmetto Key, 1942

Charles M. Breder and his wife Ethel spent part of the summer of 1942 at the Palmetto Key field station, known today as Cabbage Key, on the west coast of Florida south of Charlotte Harbor. The Palmetto Key field station began in 1938 and ended in 1942 because of World War II. His Palmetto Key diary ran for 95 pages of notes, tables, diagrams, drawings, lists, and business records and this report presents a variety of fascinating entries. Diaries from other years all bear Breder's style of discipline, curiosity, humor, and speculations on nature. The diary was transcribed as part of the Coastal Estuarine Data/Document Rescue and Archeology effort for South Florida. (PDF contaons 24 pages)