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.     

Cops and Robbers on Graphs Based on Designs

We investigate the cop number of graphs based on combinatorial designs. Incidence graphs, point graphs, and block intersection graphs are studied, with an emphasis on finding families of graphs with large cop number. We generalize known results on Meyniel extremal families by supplying bounds on the incidence graphs of transversal designs, certain G‐designs, and BIBDs with Families of graphs with diameter 2, C₄‐free, and with unbounded chromatic number are described with the conjectured asymptotically maximum cop number.     

Remarks on the Wronskian and on sums decompositions

Aequationes mathematicae - We make a number of remarks on some theorems and considerations contained in the recent and valuable monograph [9]. The connection of the Wronskian with the linear...     

基于营养健康的果蔬发展战略研究

针对果蔬品种的筛选、居民的人体营养健康状况评估及未来果蔬生产的战略调整进行研究.首先利用因子分析对果蔬的营养指标进行筛选,通过构建0-1模糊规划模型筛选出主要果蔬,并计算出果蔬的人均消费量.接着运用加权power平均(WPA)算子组合预测模型对未来果蔬消费量趋势进行预测,得到各种营养素近期及未来的人均摄入量.结果表明我国居民的部分营养摄入是不合理的,居民的营养健康状况有逐渐恶化趋势.在此基础上,建立多目标规划模型对果蔬的年度合理人均消费量进行估计,并与实际情况相比较,给出未来果蔬种植的调整战略.最后给出模型中的参数的灵敏度分析.     

基于PCA与NSSVR的人口老龄化研究

基于非线性光滑支持向量回归机研究了人口老龄化问题.首先介绍了非线性光滑支持向量回归机(NSSVR);其次,提出了人口老龄化影响体系,利用主成分分析(PCA),在体系基础上提取出对老龄化影响明显的9个指标;再次,通过非线性光滑支持向量回归机模型建立了老龄化率与9个影响指标间的相互关系;最后,用非线性光滑支持向量回归机模型对未来人口老龄率进行预测.实证表明,方法具有很好的预测效果.     

Uniform and refinable grids on elliptic domains and on some surfaces of revolution

We construct a bijection from R² to R², which maps rectangles centered at the origin O onto ellipses centered at O, and preserves area. This bijection allows us to construct uniform and refinable grids on elliptic domains. Then, we combine a particular case of this bijection (i.e. that bijection that maps squares into circles) with another area preserving projection from R² to a surface of revolution around Oz. This yields uniform and refinable grids on this surface of revolution. The lines of these grids are situated in horizontal planes, if they are images of squares centered at O. We consider the particular case of the hemisphere and show how the northern hemisphere of the Earth is projected onto a square. Thus, our equiareal maps can be useful for constructing geographical maps of one hemisphere of the Earth onto rectangles.     

Expansive flows on Seifert manifolds and on torus bundles

We show that any expansive flow on a 3-manifold which is a Seifert fibration or a torus bundle overS ¹ is topologically equivalent to a transitive Anosov flow. This is achieved by analyzing the trace of the stable foliation (with singularities) of the flow on incompressible tori embedded in such a manifold.     

Notes on flatness and the quot functor on rings

For flat modules M over a ring A we study the similarities between the three statements,dim _k (P) ( _k (P)? _A M =dfor all prime ideals P of A, the Ap-module M _p is free of rank d for all prime ideals P of A, and M is a locally free J4-module of rank d. We have particularly emphasized the case when there is an>l-algebra B, essentially of finite type, and M is a finitely generated B-module.     

Some remarks on Reid on primary and secondary qualities

John Locke’s distinction between primary and secondary qualities of objects has meet resistance. In this paper I bypass the traditional critiques of the distinction and instead concentrate on two specific counterexamples to the distinction: Killer yellow and the puzzle of multiple dispositions. One can accommodate these puzzles, I argue, by adopting Thomas Reid’s version of the primary/secondary quality distinction, where the distinction is founded upon conceptual grounds. The primary/secondary quality distinction is epistemic rather than metaphysical. A consequence of Reid’s primary/ secondary quality distinction is that one must deny the original version of Molyneux’s question, while one must affirm an amended version of it. I show that these two answers to Molyneux’s question are not at odds with current empirical research.     

A note on polylogarithms on curves and abelian schemes

In this note we study the polylogarithm extension on curves and abelian schemes in the étale realization. The main result shows that the polylog on the jacobian of a curve is given as the cup-product of the polylog on the curve with the fundamental class of the curve.     

Brownian bridge on hyperbolic spaces and on homogeneous trees

Let B be the Brownian motion on a noncompact non Euclidean rank one symmetric space H. A typical examples is an hyperbolic space H _n , n > 2. For ν > 0, the Brownian bridge B ^(ν) of length ν on H is the process B _t , 0 ≤t≤ν, conditioned by B ₀ = B _ν = o, where o is an origin in H. It is proved that the process converges weakly to the Brownian excursion when ν→ + ∞ (the Brownian excursion is the radial part of the Brownian Bridge on ℝ³). The same result holds for the simple random walk on an homogeneous tree. Received: 4 December 1998 / Revised version: 22 January 1999     

Bounded, attractive and repulsive Markov specifications on trees and on the one-dimensional lattice

Let Π be a homogenous Markov specification associated with a countable state space S and countably infinite parameter space A possessing a neighbor relation ~ such that (A,~) is the regular tree with d +1 edges meeting at each vertex. Let $\text{g}$(π)be the simplex of corresponding Markov random fields. We show that if Π satisfies a ‘boundedness’ condition then $\text{g}$(π).We further study the structure of $\text{g}$(π) when Π is either attractive or repulsive with respect to a linear ordering on S. When d = 1, so that (A, ~) is the one-dimensional lattice, we relax the requirement of homogeneity to that of stationarity; here we give sufficient conditions for $\text{g}$(π) and for $\text{g}$(π)to have precisely one member.     

Variations on cops and robbers

We consider several variants of the classical Cops and Robbers game. We treat the version where the robber can move R≥1 edges at a time, establishing a general upper bound of , where α = 1 + 1/R, thus generalizing the best known upper bound for the classical case R = 1 due to Lu and Peng, and Scott and Sudakov. We also show that in this case, the cop number of an n‐vertex graph can be as large as n^{1 ? 1/(R ? 2)} for finite R≥5, but linear in n if R is infinite. For R = 1, we study the directed graph version of the problem, and show that the cop number of any strongly connected digraph on n vertices is O(n(loglogn)²/logn). Our approach is based on expansion. © 2011 Wiley Periodicals, Inc. J Graph Theory.     

Lengths on semigroups and groups

We give a characterization of those semigroups with topology arising from a collection of left sub-invariant pseudometrics or quasimetrics. We also characterize those with topology arising from sub-invariant pseudometrics or quasimetrics.     

Sheaves and sheafification on Q-sites

We introduce noncommutative sites over a quantale, the so-called Q-sites, and define appropriate presheaves and sheaves over these. We show how most of the technical machinery which allows to construct sheaves associated to arbitrary presheaves in the commutative cases transposes to this setting. This allows us to define and study sheafification in this new, noncommutative context.     

III-Homomorphisms and III-congruences on posets

A new homomorphism between two partially ordered sets (the III-homomorphism) and a new congruence on a poset (the III-congruence) are introduced. Some properties of these homomorphisms and congruences and their relationship to the other known homomorphisms and congruences on posets are investigated. In contrast to total algebras, there are many different ways to introduce these notions. It is usually required that the respective notions should coincide with the usual definitions whenever lattices or semilattices are treated. The present paper presents an approach which in some sense completes the hierarchy of definitions so far used.