Special relativistic Fourier transformation and convolutions

In this paper, we use the steerable special relativistic (space‐time) Fourier transform (SFT) and relate the classical convolution of the algebra for space‐time Cl(3,1)‐valued signals over the space‐time vector space , with the (equally steerable) Mustard convolution. A Mustard convolution can be expressed in the spectral domain as the point wise product of the SFTs of the factor functions. In full generality do we express the classical convolution of space‐time signals in terms of finite linear combinations of Mustard convolutions and vice versa the Mustard convolution of space‐time signals in terms of finite linear combinations of classical convolutions.     

可配置高速二维卷积处理器设计与Gabor滤波应用

针对具有多种大尺寸卷积内核的Gabor滤波器组,设计了可配置二维卷积处理器来实现硬件加速。该处理器利用FPGA(field programmable gate array)内部逻辑资源构建具有多级流水线的二维卷积运算单元,并通过子块分割及重组来支持任意尺寸的卷积运算。使用高级语言对其控制器编程来实现对卷积运算单元及数据流的配置,从而实现Gabor滤波。实验表明:使用EP2C70F896C6型FPGA工作在75MHz,对于120×90像素的灰度图像计算五尺度八方向Gabor滤波(最大尺寸为41×41像素,系数为复数)总耗时28.8ms。     

一类非线性抛物方程Cauchy问题解的逼近性质

］利用基本解与初值的卷积来构造非线性方程的解, 用卷积结果来逼近其真解, 并运用Holder不等式和Taylor展开式给出了卷积结果与真解之间的误差     

Optical transfer function analysis of circular-pupil wavefront coding systems with separable phase masks

This paper proposes a simple method to achieve the optical transfer function of a circular pupil wavefront coding system with a separable phase mask in Cartesian coordinates.Based on the stationary phase method,the optical transfer function of the circular pupil system can be easily obtained from the optical transfer function of the rectangular pupil system by modifying the cut-off frequency and the on-axial modulation transfer function.Finally,a system with a cubic phase mask is used as an example to illustrate the way to achieve the optical transfer function of the circular pupil system from the rectangular pupil system.     

基于FPGA的通用卷积层IP核设计

针对目前卷积神经网络在小型化、并行化过程中遇到的计算速度不够、可移植性差的问题,根据卷积神经网络和FPGA器件的特点,提出了一种利用VHDL语言参数化高速通用卷积层IP核的设计方法。利用卷积层的计算方式,将卷积核心设计为全并行化、流水线的计算模块,通过在卷积核心的每一行连接FIFO的方式改善数据流入的方式,减少地址跳转的操作,并加入控制核心使其可以随图像和卷积窗口大小调整卷积层参数,生成不同的卷积层,最后将卷积层与AXIS协议结合并封装成IP核。结果表明,在50 MHz的工作频率下,使用2×2大小的卷积核对100×100的图像进行卷积计算,各项资源利用率不超过1%,耗时204μs,计算速度理论上可以达到最高5 MF/s。因此,设计方案在增加卷积模块可移植性的同时又保证了计算速度,为卷积神经网络在小型化器件上的实现提供了一种可行的方法。     

Offset approximation based on reparameterizing the path of a moving point along the base circle

This paper presents a novel algorithm for planar curve offsetting. The basic idea is to regard the locus relative to initial base circle, which is formed by moving the unit normal vectors of the base curve, as a unit circular arc first, then accurately to represent it as a rational curve, and finally to reparameterize it in a particular way to approximate the offset. Examples illustrated that the algorithm yields fewer curve segments and control points as well as C^1 continuity, and so has much significance in terms of saving computing time, reducing the data storage and smoothing curves entirely.     

Realizability of words in mosaic labyrinths

In this paper we study mosaic labyrinths with the help of words generated by them in the alphabet of labels attached to arcs and vertices of a labyrinth. We consider the problem of the characterization of words generated by a labyrinth. We propose a constructive recognition criterion, it defines whether a word is generated by a labyrinth or not. We establish conditions under which a word can be generated by a unique labyrinth, by a finite number of labyrinths, or by infinitely many labyrinths.     

Efficient Implementation of a Spectral-Tau Method for a Class of Two-Point Boundary-Value and Initial-Boundary-Value Problems

A simple and efficient spectral method for solving the second, third order and fourth order elliptic equations with variable coefficients and nonlinear differential equations is presented. It is different from spectral-collocation method which leads to dense, ill-conditioned matrices. The spectral method in this paper solves for the coefficients of the solution in a Chebyshev series, leads to discrete systems with special structured matrices which can be factorized and solved efficiently. We also extend the method to boundary value problems in two space dimensions and solve 2-D separable equation with variable coefficients. As an application, we solve Cahn-Hilliard equation iteratively via first-order implicit time discretization scheme. Ample numerical results indicate that the proposed method is extremely accurate and efficient.     

Trace theorems for functions of bounded variation in metric spaces

In this paper we show existence of traces of functions of bounded variation on the boundary of a certain class of domains in metric measure spaces equipped with a doubling measure supporting a 1-Poincaré inequality, and obtain $L^1$ estimates of the trace functions. In contrast with the treatment of traces given in other papers on this subject, the traces we consider do not require knowledge of the function in the exterior of the domain. We also establish a Maz'ya-type inequality for functions of bounded variation that vanish on a set of positive capacity.     

A backward Euler alternating direction implicit difference scheme for the three‐dimensional fractional evolution equation

A backward Euler alternating direction implicit (ADI) difference scheme is formulated and analyzed for the three‐dimensional fractional evolution equation. In our method, the Riemann‐Liouville fractional integral term is treated by means of first order convolution quadrature suggested by Lubich. Meanwhile, an ADI technique is adopted to reduce the multidimensional problem to a series of one‐dimensional problems. A fully discrete difference scheme is constructed with space discretization by finite difference method. Two new inner products and corresponding norms are defined to analyze the scheme. The verification of stability and convergence is based on the nonnegative character of the real quadratic form associated with the convolution quadrature. Numerical experiments are reported to demonstrate the efficiency of our scheme.