INCOMPRESSIBLE PAIRWISE INCOMPRESSIBLE SURFACES IN LINK COMPLEMENTS

The central subject of studying in this paper is incompressible pairwise incompressible surfaces in link complements. Let L be a non-split prime link and let F be an incompressible pairwise incompressible surface in S3 - L. We discuss the properties that the surface F intersects with 2-spheres in S3 - L. The intersection forms a topological graph consisting of a collection of circles and saddle-shaped discs. We introduce topological graphs and their moves （R-move and S2-move）, and define the characteristic number of the topological graph for F∩S2±. The characteristic number is unchanged under the moves. In fact, the number is exactly the Euler Characteristic number of the surface when a graph satisfies some conditions. By these ways, we characterize the properties of incompressible pairwise incompressible surfaces in alternating （or almost alternating） link complements. We prove that the genus of the surface equals zero if the component number of F∩S2＋（or F∩S2-） is less than five and the graph is simple for alternating or almost alternating links. Furthermore, one can prove that the genus of the surface is zero if #（F） ≤8.

Incompressible Surfaces in Almost Alternating Link Exteriors

In this paper, we discuss mainly the properties of incompressible pairwise incomprcssiblc surfaccs in ahnost altcrnating link complcmcnts. Lct L bc a almost link and lct F be an incompressible pairwise incompressible surface in S^3 - L. First, we give the properties that the surface F intersects with 2-spheres in S^3- L. The intersection consisting of a collection of circles and saddle-shaped discs is called a topological graph. One can compute the Euler Characteristic number of the surface by calculating the characteristic number of the graph. Next, we prove that if the graph is special simple, then the genus of the surface is zero.

Delimitation of Countries,Regions and Cities Which the Tropic of Cancer Traverses and Its Development Strategies

The central value 23°26′17″ of the Tropic of Cancer is used for delimiting the standard position of the Tropic of Cancer as well as countries, regions and cities which the Tropic of Cancer traverses. It is confirmed that the Tropic of Cancer runs through 19 countries and regions in the world, and it traverses Yunnan, Guangxi, Guangdong, Fujian （sea area） and Taiwan provinces in China. At the same time, regions which the Tropic of Cancer traverses are divided into three regions, namely the extensive Tropic of Cancer region, the Tropic of Cancer region and the core area of the Tropic of Cancer. The series of delimitation and division aims to explore ways of sustainable development under the restriction of resources and environment and build collaborative development areas of the Tropic of Cancer at all leaves, especially setting up the collaborative de- velopment zone of the Tropic of Cancer in China and international collaborative development circle of the Tropic of Cancer.

Application advances of catheter modification in difficult coronary artery Intervention

Background Judkins catheter is widely used in recent years, for clinical angiography and intervention of most normal coronary arteries, but still incapable to deal with the problems caused by difficult coronary artery （DCA）. DCA may influence the procedure of diagnosis and intervention of ischemic heart disease （IHD）. To cope with different subtypes of DCA, catheters like Amplatz, EBU, Leya, etc. were born at that moment, but these stan- dard catheters are used just in special cases and have so many sequences that a local hospital may not be able to keep all of them available routinely at any time. To overcome this problem, some centers perform angiography and intervention using modified catheters based on their own condition and have obtained some experiences. Catheter modification techniques used in these years are reviewed, and are stated respectively based on dealing with different subtypes of DCA to provide practical guidance for clinical diagnosis and intervention for IHD patients having DCA.