实现金相图象彩色化的一种新方法

本文提出一种简便的方法,仅利用一彩色滤波器便可以从金相显微镜实时地观察到假彩色编码图象。图象棱角分明、色彩鲜艳丰富,并能显示黑白显微放大图象所看不到的细节。 我们使用的方法是使黑白图象假彩色化,它利用改造物的空间频谱(即在不同频谱处仅让“某种颜色的光”通过)而实现的。 作者给出理论解析、实验装置和实验结果,并指出这种方法的优点及其在冶金,机械等领域的潜在实用前景。     

A note of a modular equation of Ramanujan–Selberg continued fraction

The Ramanujan Journal - We show that if $$E/\mathbb {Q}$$ is an elliptic curve with a rational p-torsion for $$p=2$$ or 3, then there is a congruence relation between Ramanujan’s tau function...     

The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-field Stochastic Differential Equations

In this paper, some properties of a stochastic convolution driven by tempered fractional Brownian motion are obtained. Based on this result, we get the existence and uniqueness of stochastic mean-field equation driven by tempered fractional Brownian motion. Furthermore, combining with the Banach fixed point theorem and the properties of Mittag-Leffler functions, we study the existence and uniqueness of mild solution for a kind of time fractional mean-field stochastic differential equation driven by tempered fractional Brownian motion.     

Film digitization aliasing artifacts caused by grid line patterns

Sampling a radiographic film containing grid line patterns during digitization may produce aliasing artifacts (Moire pattern). The authors propose a mathematical model based on the laser spot size of the digitizer, the distance and the angle between the grid line and the sampling direction to predict the amplitudes and the frequencies of aliasing artifacts. The predicted results are compared to the experimental results. Effective ways of avoiding or reducing aliasing artifacts without sacrificing too much image quality are proposed.     

Optimal Control of an <Emphasis Type="Italic">M/E</Emphasis><Subscript><Emphasis Type="Italic">k</Emphasis></Subscript>/1 Queueing System with a Removable Service Station

This paper studies the optimal operation of an M/E _k /1 queueing system with a removable service station under steady-state conditions. Analytic closed-form solutions of the controllable M/E _k /1 queueing system are derived. This is a generalization of the controllable M/M/1, the ordinary M/E _k /1, and the ordinary M/M/1 queueing systems in the literature. We prove that the probability that the service station is busy in the steady-state is equal to the traffic intensity. Following the construction of the expected cost function per unit time, we determine the optimal operating policy at minimum cost.     

A theory of tensor products for module categories for a vertex operator algebra,I

This is the first part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a vertex tensor category structure on the category of modules for a suitable vertex operator algebra. The notion of vertex tensor category is essentially a complex analogue of the notion of symmetric tensor category, and in fact a vertex tensor category produces a braided tensor category in a natural way. The theory applies in particular to many familiar rational vertex operator algebras, including those associated with WZNW models, minimal models and the moonshine module. In this paper (Part I), we introduce the notions ofP(z)- andQ(z)-tensor product, whereP(z) andQ(z) are two special elements of the moduli space of spheres with punctures and local coordinates, and we present the fundamental properties and constructions ofQ(z)-tensor products.     

Boundedness of solutions of nonlinear systems of differential equations

We first give an example to illustrate that the results in [12] concerning the boundedness of solutions of nonlinear oscillatory equations are not true. And then we obtain sufficient or necessary conditions for the boundedness of solutions of the nonlinear system of differential equations