Deciding confluence of certain term rewriting systems in polynomial time

We present a characterization of confluence for term rewriting systems, which is then refined for special classes of rewriting systems. The refined characterization is used to obtain a polynomial time algorithm for deciding the confluence of ground term rewrite systems. The same approach also shows the decidability of confluence for shallow and linear term rewriting systems. The decision procedure has a polynomial time complexity under the assumption that the maximum arity of a function symbol in the signature is a constant.     

Rank, term rank, and chromatic number

Let G be a graph with a nonempty edge set, and with rank rk(G), term rank Rk(G), and chromatic number χ(G). We characterize Rk(G) as being the maximum number of colors in certain proper colorings of G. In particular, we observe that χ(G)Rk(G), with equality holding if and only if (besides isolated vertices) G is either complete or a star. For a twin-free graph G, we observe the bound and we show that this bound is sharp.     

怎样写论文摘要

除论文标题之外 ,读者是通过摘要来决定是否继续阅读整篇论文 .因而摘要是一篇论文的窗口 .要在最小的空间内阐述问题、描述方法、总结贡献 ,是需要运用技巧与经验的 .一、摘要的内容摘要 (包括中、英文摘要 )的内容应包括目的、方法、结果、结论四个部分。重点应突出文章在结果和结论方面的创新之处 .二、摘要长度中文摘要长度一般不超过 30 0字 ,不少于 2 0 0字 ;英文摘要应比中文摘要有所扩展 ,以便使非汉语读者更多地了解文章的内容 .长度一般不超过 15 0 words,不少于 10 0 words。少数情况允许例外 ,但主题概念不得遗漏 .为了使在较短…     

On the universal Gröbner bases of toric ideals of graphs

The universal Gröbner basis of an ideal is a Gröbner basis with respect to all term orders simultaneously. We characterize in graph theoretical terms the elements of the universal Gröbner basis of the toric ideal of a graph. We also provide a new degree bound. Finally, we give examples of graphs for which the true degrees of their circuits are less than the degrees of some elements of the Graver basis.     

The expectation hypothesis of interest rates and network theory: The case of Brazil

This paper investigates the topological properties of the Brazilian term structure of interest rates network. We build the minimum spanning tree (MST), which is based on the concept of ultrametricity, using the correlation matrix for interest rates of different maturities. We show that the short-term interest rate is the most important within the interest rates network, which is in line with the Expectation Hypothesis of interest rates. Furthermore, we find that the Brazilian interest rates network forms clusters by maturity.     

On an Error Term Related to the r-th Power of the Euler Totient Function

ＯｎａｎＥｒｒｏｒＴｅｒｍＲｅｌａｔｅｄｔｏｔｈｅｒ－ｔｈＰｏｗｅｒｏｆｔｈｅＥｕｌｅｒＴｏｔｉｅｎｔＦｕｎｃｔｉｏｎＬｉｕＪｉａｎｙａ（刘建亚）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｄｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｊｉｎａｎ，２５...     

Pricing range notes within Wishart affine models

We provide analytic pricing formulas for Fixed and Floating Range Accrual Notes within the multifactor Wishart affine framework which extends significantly the standard affine model. Using estimates for three short rate models, two of which are based on the Wishart process whilst the third one belongs to the standard affine framework, we price these structured products using the FFT methodology. Thanks to the Wishart tractability the hedge ratios are also easily computed. As the models are estimated on the same dataset, our results illustrate how the fit discrepancies (meaning differences in the likelihood functions) between models translate in terms of derivatives pricing errors, and we show that the models can produce different price evolutions for the Range Accrual Notes. The differences can be substantial and underline the importance of model risk both from a static and a dynamic perspective. These results are confirmed by an analysis performed at the hedge ratios level.     

一类反应扩散方程的行波解

1　引　　言由于反应扩散方程涉及的大量问题来自物理学、化学、生物学和人口动力学中众多的数学模型,因而有广阔的实际背景.其行波解引起了人们的兴趣,行波解是某个常微分方程的解,对某些传播速度,利用几何方法可以建立其解的存在性(见[1][2][3]).在文[4]中J.Canosa讨论了Fisher方程ut=2u2x+u(1-u)(1)行波解的存在性、逼近解和误差估计.所谓方程(1)的行波解是指形为u(x,t)=u(x-ct)=u(z)的解.众所周知,行波解u(x,t)=u(x-ct)=u(z)是方程(1)的行波解的充要条件是d2udz2+cdudz+u(1-u)=0(2)若u(z)是单调有界且不恒为常数,则u(z)叫做(1)的波前…     

Some results on strong solutions of SDEs with applications to interest rate models

In this work, we investigate SDEs whose coefficients may depend on the entire past of the solution process. We introduce different Lipschitz-type conditions on the coefficients. It turns out that for existence and uniqueness of a strong solution it suffices to have Lipschitz continuity in mean, in a sense to be made precise. We then investigate when it suffices to have local Lipschitz conditions. Furthermore we consider the case of drift coefficients which are locally Lipschitz in mean. Finally we show how these results can be applied to prove existence and uniqueness of solutions in interest rate term structure models.     

局域强组态相互作用对类氖离子AlⅣ－TiⅩⅢ2s~22p~55f能级结构及跃迁的影响

用相对论组态相互作用方法，分析了类氖离子ＡｌⅣ－ＴｉⅩⅢ偶宇称态２ｓ２ｐ６３ｌ与２ｓ２２ｐ５５ｌ之间的组态相互作用及其对２ｓ２２ｐ５５ｆ能级结构及跃迁的影响；给出了无实验结果的２ｐ５５ｆ能级值和较强２ｓ２２ｐ５５ｆ－２ｓ２２ｐ５４ｄ、２ｓ２２ｐ５５ｆ－２ｓ２２ｐ５５ｄ跃迁的波长及根子强度