More on cancellative semigroups on manifolds

Communicated by D.R.Brown     

基于学习—遗忘效应的生产率降低损失索赔研究

建设工程项目很多具有重复性施工的特点,本文利用这种特点将学习-遗忘效应应用到平衡作业线(LOB)方法中,分析因为工程中断造成生产率的降低的现象,认为因生产率降低而导致工程工期的延长实际上超过工程实际中断的时间,最后以一个工程案例来说明分析过程.     

Remarks on continuum cardinals on Boolean algebras

We give some results concerning various generalized continuum cardinals. The results answer some natural questions which have arisen in preparing a new edition of 5 . To make the paper self‐contained we define all of the cardinal functions that enter into the theorems here. There are many problems concerning these new functions, and we formulate some of the more important ones.     

Remark on the weierstrass points on curves

We give a treatment of the Weiertrass points of curves which is a little different from the treatment by Laksov. We introduce the notion of theith weight which makes the treatment easier and gives an algorithm for computing the gap sequence of an effective divisor and the weight at a point. Supported in part by NNSF of China.     

Remarks on normal operators on Banach spaces

Rendiconti del Circolo Matematico di Palermo Series 2 - A closed densely defined operatorT on a Banach spaceX is called normal, iff $$T \in [C^0 (\hat \not C)]$$ , i.e. there is a homomorphism...     

A note on pseudo-metrics on the plane

Every c-finite measure Μ on the set G of the lines on the plane such that $$(0){\text{ }}\mu {\text{(\{ g}} \in G:{\text{ }}P \in {\text{g\} ) = 0}}$$ for every point P?R ² generates a pseudo-metric F on the plane when one puts F P ₁, P ₂= \(\tfrac{1}{2}\) μ({g∈G:g separates the points P ₁ and P ₂}) The pseudo-metrics which are generated in this way possess the property of linear additivity, that is F(P ₁,P ₃)=F(P ₁,P ₂)+F(P ₂,P ₃) for P ₁,P ₂,P ₃ on a line, P ₂ between P ₁ and P ₃, and are continuous with respect to the Euclidean topology in R ² × R ². In this paper we prove the converse: every linear additive and continuous pseudo-metric F is generated as above by some c-finite measure Μ on G for which (0) holds. The method of proof shows that values of linearly additive and continuous pseudo-metric F inside every bounded convex polygon C are determined completely by the values of F on (δC)². The representation of pseudo-metrics by measures is useful in derivation of inequalities for the former.     

Remarks on contact relations on Boolean algebras

The paradigmatic example for a contact relation is that of having nondisjoint closures for regions in n-dimensional space. Generally, a contact relation is a binary relation on a Boolean algebra reflecting some of the properties of this example. We prove in this paper a topological and an algebraic representation theorem for contact algebras and solve two problems due to Düntsch and Winter and to Dimov and Vakarelov, respectively.     

Remarks on uniform bundles on projective spaces

On projective spaces of dimension \(d\ge 2\) defined over a field of positive characteristic we construct rank \(d+1\) uniform toric but non-homogeneous bundles, which do not exists in characteristic zero. These bundles are obtained by choosing suitable equivariant extensions of the Frobenius pullbacks of \(T_{\mathbb {P}^d}\) by a line bundle.     

A note on circle patterns on surfaces

In this paper we give two different proofs of Bobenko and Springborn’s theorem of circle pattern: there exists a hyperbolic (or Euclidean) circle pattern with proscribed intersection angles and cone angles on a cellular decomposed surface up to isometry (or similarity). This work is partially supported by NSF Grant #0625935.     

Dualities and reciprocities on graphs on surfaces

We extend the duality between acyclic orientations and totally cyclic orientations on planar graphs to dualities on graphs on orientable surfaces by introducing boundary acyclic orientations and totally bi-walkable orientations. In addition, we provide a reciprocity theorem connecting local tensions and boundary acyclic orientations. Furthermore, we define the balanced flow polynomial which is connected with tension polynomial by duality and with totally bi-walkable orientations by reciprocity.     

Remarks on subharmonic functions on riemannian manifolds

Sunto Si prova un teorema di limitatezza per funzioni subarmoniche su una varietà riemanniana completa M e soddisfacenti la condisione (A) (cfr. anche [8])e se ne danno alcune applicazioni allo studio del volume di M, dello spazio delle forme armoniche a coefficienti in fibrati vettoriali su M, di cette mappe armoniche definite su M.     

Remarks on curvature dimension conditions on graphs

We show a connection between the \(CDE'\) inequality introduced in Horn et al. (Volume doubling, Poincaré inequality and Gaussian heat kernel estimate for nonnegative curvature graphs. arXiv:1411.5087v2, 2014) and the \(CD\psi \) inequality established in Münch (Li–Yau inequality on finite graphs via non-linear curvature dimension conditions. arXiv:1412.3340v1, 2014). In particular, we introduce a \(CD_\psi ^\varphi \) inequality as a slight generalization of \(CD\psi \) which turns out to be equivalent to \(CDE'\) with appropriate choices of \(\varphi \) and \(\psi \). We use this to prove that the \(CDE'\) inequality implies the classical CD inequality on graphs, and that the \(CDE'\) inequality with curvature bound zero holds on Ricci-flat graphs.     

Remark on Herz-Schur multipliers on free groups

Mathematische Annalen -