Fast radix-p discrete cosine transform

A new fast radix-p-algorithm (p 2) for the discrete cosine transform (DCT) and its inverse is presented. It is based on the divide-and-conquer method and on the arithmetic with Chebyshev polynomials. The algorithm can be applied for the efficient calculation of DCT's of arbitrary transform lengths and for the implementation of other discrete Vandermonde transforms withO(N logN) arithmetical operations.     

ON GENERALIZED FRACTIONAL PROCESSES

Abstract. A class of stationary long-memory processes is proposed which is an extension of the fractional autoregressive moving-average (FARMA) model. The FARMA model is limited by the fact that it does not allow data with persistent cyclic (or seasonal) behavior to be considered. Our extension, which includes the FARMA model as a special case, makes use of the properties of the generating function of the Gegenbauer polynomials, and we refer to these models as Gegenbauer autoregressive moving-average (GARMA) models. While the FARMA model has a peak in the spectrum at f = 0, the GARMA process can model long-term periodic behavior for any frequency 0 f 0.5. Properties of the GARMA process are examined and techniques for generation of realizations, model identification and parameter estimation are proposed. The use of the GARMA model is illustrated through simulated examples as well as with classical sunspot data.     

A data porting tool for coupling models with different discretization needs

The presented work is part of a larger research program dealing with developing tools for coupling biogeochemical models in contaminated landscapes. The specific objective of this article is to provide researchers with a data porting tool to build hexagonal raster using information from a rectangular raster data (e.g. GIS format). This tool involves a computational algorithm and an open source software (written in C). The method of extending the reticulated functions defined on 2D networks is an essential key of this algorithm and can also be used for other purposes than data porting. The algorithm allows one to build the hexagonal raster with a cell size independent from the geometry of the rectangular raster. The extended function is a bi-cubic spline which can exactly reconstruct polynomials up to degree three in each variable. We validate the method by analyzing errors in some theoretical case studies followed by other studies with real terrain elevation data. We also introduce and briefly present an iterative water routing method and use it for validation on a case with concrete terrain data.     

Algorithms for Quantum Branching Programs Based on Fingerprinting

In the paper, we develop a method for constructing quantum algorithms for computing Boolean functions by quantum ordered read-once branching programs (quantum OBDDs). Our method is based on ˉngerprinting technique and representation of Boolean functions by their characteristic polynomials. We use circuit notation for branching programs for desired algorithms presentation. For several known functions our approach provides optimal QOBDDs. Namely we consider such functions as MODm, EQn, Palindromen, and PERMn (testing whether given Boolean matrix is the Permutation Matrix). We also propose a generalization of our method and apply it to the Boolean variant of the Hidden Subgroup Problem.     

团簇态的概率隐形传送(英文)

提出一个传送未知团簇态的方案.在这个方案中,传送者利用一个非最大的三粒子纠缠态和一个非最大的四粒子纠缠态作为量子通道,当接收者执行适当的幺正操作时,可以以一定的概率完成未知团簇态的量子隐形传送.     

基于Legendre多项式展开的双基SAR二维频域成像算法

针对任意构型双基SAR基于传统Taylor级数展开斜距方法的边缘点散焦问题,提出了一种基于Legendre正交多项式逼近的双基SAR二维频域成像算法。该算法基于对斜距函数的Legendre多项式展开推导了点目标二维频谱,解除了回波信号距离—方位的耦合,使成像处理更高效。在二维频域对场景区域的点目标采用二维频域成像算法进行成像。该算法改善了场景边缘点的聚焦效果,增加了场景边缘点的聚焦深度。理论推导和仿真结果验证了该算法的有效性和可行性。     

多项式方程区间内重根的快速判定和裁剪

目的多项式求实根问题有着广泛的应用。改进传统的裁剪方法,在多项式重根的情形下,保持计算稳定性的同时显著地提高相应的收敛阶。方法提出了基于R~3空间内的3次裁剪方法。该方法继承了传统裁剪求根方法的优点,充分利用了Bernstein基函数较好的计算稳定性,同时给出简单方法判别重根的存在性,从而使得重根的情形可以转化为单根的情形。结果与已有的基于R~1和R~2空间的3次裁剪方法相比,本文方法可以具有更好的逼近效果。单根情形下,本文方法与基于R~2空间的3次裁剪方法同时具有5次收敛阶,略高于基于R~1空间3次裁剪方法的4次收敛阶;m(≥2)重根情形下,本文方法理论上可具有5次收敛阶,明显优于已有的基于R~1和R~2空间的3次裁剪方法的4/m或5/m收敛阶。基于R~1,R~2和R~3空间的3次裁剪方法的计算时间复杂度大致相当,均为O(n~2)。结论本文方法可以快速判定重根的情形,同时具有更高的收敛阶和更好的逼近效果。