Fiber Coefficients and Depth of Fiber Cones

Let (R, 𝔪) be a Cohen–Macaulay local ring of dimension d > 0, I an 𝔪-primary ideal of R, and K an ideal containing I. When r(I | K)<∞, we give a lower bound and an upper bound for f ₁(I). Under the above assumption on r(I | K) and depth G(I) ≥ d ? 1, we also provide a characterization, in terms of f ₁(I), of the condition depth F _K (I) ≥ d ? 1.     

On Fiber Coefficients of Fiber Cones †

Let (R,𝔪) be a Cohen–Macaulay local ring of dimension d > 0, I an 𝔪-primary ideal of R, and K an ideal containing I. When depth G(I) ≥ d ? 1, depth F_K(I) ≥ d ? 2, and r(I|K) < ∞, we calculate the fiber coefficients f_i(I). Under the above assumptions on depth G(I) and r(I|K), we give an upper bound for f₁(I), and also provide a characterization, in terms of f₁(I), of the condition depth F_K(I) ≥ d ? 2.     

关于纤维锥的Hilbert系数

Let （R, m） be a Cohen-Macaulay local ring of dimension d, I an mprimary ideal and K an ideal containing I. Assuming that I has minimal （almost minimal） mixed multiplicity with respect to K, we get some results on the Hilbert coefficients of fiber cones.     

On the Multiplicity and the Cohen-Macaulayness of Fiber Cones of Graded Modules

Let (A,m) be a Noetherian local ring with maximal ideal m,I an ideal of A,J an m-primary ideal of A,N a finitely generated A-module,S =⊕n≥0 Sn a finitely generated standard graded algebra over A and M =⊕n≥0 Mn a finitely generated graded S-module.We characterize the multiplicity and the Cohen-Macaulayness of the fiber cone FJ(M) =⊕n≥0 Mn/JMn.As an application,we obtain some results on the multiplicity and the Cohen-Macaulayness of the fiber cone ⊕n≥0 InN/JInN.     

A Lower Bound for the Rectilinear Crossing Number

We give a new lower bound for the rectilinear crossing number of the complete geometric graph K_n. We prove that and we extend the proof of the result to pseudolinear drawings of K_n. Dedicated to the memory of our good friend and mentor Víctor Neumann-Lara. Received: April, 2003 Final version received: March 18, 2005     

Properties of the Fiber Cone of Ideals in Local Rings

Abstract

For an ideal I of a Noetherian local ring (R, m ) we consider properties of I and its powers as reflected in the fiber cone F(I) of I. In particular,we examine behavior of the fiber cone under homomorphic image R → R/J = R′ as related to analytic spread and generators for the kernel of the induced map on fiber cones ψ _J  : F _R (I) → F _R′(IR′). We consider the structure of fiber cones F(I) for which ker ψ _J  ≠ 0 for each nonzero ideal J of R. If dim F(I) = d > 0,μ(I) = d + 1 and there exists a minimal reduction J of I generated by a regular sequence,we prove that if grade(G ₊(I)) ≥ d ? 1,then F(I) is Cohen-Macaulay and thus a hypersurface.     

赋范线性空间中包含方程可解性定理的推广及弱切锥的应用

本文首先在一般的赋范线性空间中研究了集值映射F;X→Y的平衡点的存在性问题,证明了包含问题O∈F(X)的三个可解性定理.然后在无穷维空间中研究了弱相依锥T_k^σ(x)的直接像,弱相依导数D^σF(x,y)的一个链式法则以及偏y弱导数D_y^σF(x,y)的弱Lip连续性.最后,作为应用,给出并证明了用弱相依导数D^σF(x,y)及弱P导数P^σF(x,y)判定无穷维     

A Lower Bound on Unknotting Number

In this paper the authors use a modified Wirtinger presentation to give a lower bound on the unknotting number of a knot in S3.     

纤维悬浮剪切湍流中纤维旋转扩散系数的理论研究

对纤维悬浮剪切湍流中纤维旋转扩散系数进行了理论研究．首先建立了流场不同脉动速度梯度间的相关矩函数,然后推导出了纤维旋转扩散系数的表达式,该表达式依赖于特征长度、时间、速度和一个与壁面作用相关的无量纲参数．得到的纤维旋转扩散系数可以应用于非均匀和非各向同性的湍流场,此外还可以推广到三维湍流场,因而为纤维悬浮湍流场的研究提供了理论基础．     

局部β-凸空间中的第二分离性定理及其共轭锥上的有界性定理

第一部分给出局部β－凸空间中的第二分离性定理和Ｍｉｎｋｏｗｓｋｉ定理及Ｋｒｅｉｎ－Ｍｉｌｍａｎ定理等；第二部分得到其共轭锥上Ｕ Ｆ－有界与Ｕ Ｂ－有界等价的充要条件为原空间是次完备的．     

Bessel变换的一个下界

Bessel逆问题在物理、化学和工程学等诸多领域有重要应用.解决线性逆问题的传统方法不适合处理具有奇异性曲线边缘的二元函数.鉴于切波对这一类函数的最优表示能力,相关文献采用切波方法研究Bessel逆问题,构造了目标函数的切波域值估计器,得到了它在函数空间V中积分均方差收敛阶的上界.在此基础上利用统计理论给出其最小最大风险的一个下界,证明了在估计Bessel逆问题时此估计器是最优的.     

Smarandache函数在两数列上的下界估计

设S(n)是Smarandache函数,其中n是一正整数.讨论Smarandache函数S(n)在数列F((2k),1)=F(n,1)=n2n+1(n=2k)与数列G(2n,1)=(2n)2n+1上的下界估计.基于初等方法证明了:当偶数n≥6时,有S(F((2k),1))=S(F(n,1))≥6×2n+1;当n≥4时,有S(G(2n,1))≥6×2n+1.     

A Lower Bound on the Greedy Weights of Product Codes

A greedy 1-subcode is a one-dimensional subcode of minimum (support) weight. A greedy r-subcode is an r-dimensional subcode with minimum support weight under the constraint that it contain a greedy (r - 1)-subcode. The r-th greedy weight e _r is the support weight of a greedy r-subcode. The greedy weights are related to the weight hierarchy. We use recent results on the weight hierarchy of product codes to develop a lower bound on the greedy weights of product codes.     

A Lower Bound on the Growth of Word Hyperbolic Groups

We give a linear lower bound on the exponential growth rateof a non-elementary subgroup of a word hyperbolic group, withrespect to the number of generators for the subgroup.     

Orlicz序列空间的粗系数

证明了Orlicz序列空间lm的粗系数R（lm）=2／supky,这里‖y‖0n=1ky=min{k＞0：‖y‖0n=1/k（1＋PN（ky））}．     

第Ⅱ类非自共轭锥上的Gamma函数

本文将Ｇａｍｍａ函数及Ｓｉｅｇｅｌ积分推广到一般的第Ⅱ类非自共轭锥上,作为其应用,显示给出了以这些锥为底的管状域的Ｃａｕｃｈｙ－Ｓｚｅｇｏｅ核和形式Ｐｏｉｓｓｏｎ核。     

A note on the convexity assumption of possibilistic correlation

In 2005, Carlsson, Fullér and Majlender introduced a measure of possibilistic correlation of fuzzy numbers A and B by their joint possibility distributionC as an average degree of interaction between the γ-level sets of A and B as compared to their individual dispersions. They proved that this possibilistic correlation coefficient can never exceed 1 in absolute value, if all γ-level sets of the joint possibility distribution C are convex.In this communication, we shall formulate a special class of joint possibility distributions with non-convex γ-level sets, for which the correlation coefficient can take values outside the interval [−1,1]. In particular, this result will show that the assumption about the convexity of the level sets of C is essential for the possibilistic correlation to be bounded by the interval [−1,1].     

A New Lower Bound on the Potential-Ramsey Number of Two Graphs

A nonincreasing sequence π=(d₁,…,d_n) of nonnegative integers is a graphic sequence if it is realizable by a simple graph G on n vertices.In this case,G is referred to as a realization of π.Given a graph H,a graphic sequence π is potentially H-graphic if π has a realization containing H as a subgraph.For graphs G₁ and G₂,the potential-Ramsey number r_pot(G₁,G₂) is the smallest integer k such that for every k-term graphic ...