Financial heat machine

We consider dynamics of financial markets as dynamics of expectations and discuss such a dynamics from the point of view of phenomenological thermodynamics. We describe a financial Carnot cycle and the financial analog of a heat machine. We see, that while in physics a perpetuum mobile is absolutely impossible, in economics such mobile may exist under some conditions.     

扬州瘦西湖风景区客源市场空间结构研究

将扬州瘦西湖风景区与国内其它旅游风景区客源空间结构进行比较，运用距离累积曲线及方向雷达图等手段，研究扬州瘦西湖风景区客源市场空间结构特征。研究表明，扬州瘦西湖对近中程距离客源地游客具有较大的吸引力，提出了风景旅游地吸引距离范围的定量评价办法，指出按客源地划分的入游游客人数的方向雷达图是研究旅游地客源市场空间结构方向变异的有效工具。     

A characterization of the interval distance monotone graphs

A simple connected graph G is said to be interval distance monotone if the interval I(u,v) between any pair of vertices u and v in G induces a distance monotone graph. A?¨der and Aouchiche [Distance monotonicity and a new characterization of hypercubes, Discrete Math. 245 (2002) 55-62] proposed the following conjecture: a graph G is interval distance monotone if and only if each of its intervals is either isomorphic to a path or to a cycle or to a hypercube. In this paper we verify the conjecture.     

Further mathematical properties of Cayley digraphs applied to hexagonal and honeycomb meshes

In this paper, we extend known relationships between Cayley digraphs and their subgraphs and coset graphs with respect to subgroups to obtain a number of general results on homomorphism between them. Intuitively, our results correspond to synthesizing alternative, more economical, interconnection networks by reducing the number of dimensions and/or link density of existing networks via mapping and pruning. We discuss applications of these results to well-known and useful interconnection networks such as hexagonal and honeycomb meshes, including the derivation of provably correct shortest-path routing algorithms for such networks.     

An improved hybrid Cartesian/immersed boundary method for fluid–solid flows

An improved hybrid Cartesian/immersed boundary method is proposed based on ghost point treatment. A second‐order Taylor series expansion is used to evaluate the values at the ghost points, and an inverse distance weighting method to interpolate the values due to its properties of preserving local extrema and smooth reconstruction. The present method effectively eliminates numerical instabilities caused by matrix inversion and flexibly adopts the interpolation in the vicinity of the boundary. Some typical fluid–solid flows, including viscous flow past a circular cylinder, a sphere, two cylinders in a side‐by‐side arrangement, and an array of 18 staggered cylinders, are examined. These benchmark simulations reasonably indicate the reliability and capability of the present method. Copyright © 2007 John Wiley & Sons, Ltd.     

Equipartite Gregarious 5-Cycle Systems and Other Results

A k-cycle decomposition of a complete multipartite graph is said to be gregarious if each k-cycle in the decomposition has its vertices in k different partite sets. Equipartite 3-cycle systems are 3-GDDs (and so are automatically gregarious), and necessary and sufficient conditions for their existence are known. The cases of equipartite gregarious 4-, 6- and 8-cycle systems have also been dealt with (using techniques that could be applied in the case of any even length cycle). Here we give necessary and sufficient conditions for the existence of a gregarious 5-cycle decomposition of the complete equipartite graph K_m(n) (in effect the first odd length cycle case for which the gregarious constraint has real meaning). In doing so, we also define some general cyclic constructions for the decomposition of certain complete equipartite graphs into gregarious p-cycles (where p is an odd prime).     

ON 3-CHOOSABIL ITY OF PL ANE GRAPHSON3 -CHOOSABIL ITY OF PL ANE GRAPHS WITHOUT 6-,7-AND 9-CYCLES

§ 1　 IntroductionAll graphs considered in this paper are finite,simple plane graphs.G=(V,E,F)denotes a plane graph,with V,E and F being the set of vertices,edges and faces of G,respectively.Two vertices u and v are adjacent,denoted by uv∈E,if there is an edge in Ejoining them.A vertex u is incident with an edge e if u is an endvertex of e.Two faces aresaid to be adjacent if they share a common edge.We use b(f) to denote the boundary of aface f.A face is incident with all vertices and e…     

Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four

A class of degree four differential systems that have an invariant conic x ² + Cy ² = 1, C ∈ ℝ, is examined. We show the coexistence of small amplitude limit cycles, large amplitude limit cycles, and invariant algebraic curves under perturbations of the coefficients of the systems.     

Big Heegaard distance implies finite mapping class group

We show that if M is a closed three manifold with a Heegaard splitting with sufficiently big Heegaard distance then the subgroup of the mapping class group of the Heegaard surface, whose elements extend to both handlebodies is finite. As a corollary, this implies that under the same hypothesis, the mapping class group of M is finite.     

Planar graphs without 4,6,8-cycles are 3-colorable

In this paper we prove that every planar graph without 4,6 and 8-cycles is 3-colorable.