View Of Topology Research Articles

巨大フラーレンの構造の位相幾何学的考察

The structures of giant fullerenes have been considered from the topological view point. As the fullerenes are formed of the pentagonal rings and hexagonal rings, Euler's theorem in the topology shows that 12 pentagonal rings are neccessary though the number of hexagonal ones is arbitrary for the formation of the closed polyhedron. This restraint predicts that symmetric giant fullerenes have the following shapes: the icosahedral-shaped, the tetrahedral-shaped, the pentagonal prism-shaped and the hexagonal prism-shaped ones. We have classified the icosahedral-shaped and the tetrahedral-shaped ones into three systems, respectively, and the pentagonal prism-shaped and the hexagonal prism-shaped ones into two systems, respectively, thus totaling ten systems. We have formulated the equations for calculating the number of atoms n in the giant fullerenes Cn. The results indicate that the forming of the round-shaped giant fullerenes requires the sets of heptagonal and pentagonal rings while keeping (the number of pentagonal rings)-(the number of heptagonal rings)=12.

Host-guest binding in two coordinatoclathrates of 1,1?-binaphthyl-2,2?-dicarboxylic acid. x-ray crystal structures of the inclusion compounds with 1-propanol (2 : 1) andt-butanol (1 : 1)

1,1'-Binaphthyl-2,2'-dicarboxylic acid (1) forms crystalline inclusion compounds with 1-PrOH (2:1) andt-BuOH (1:1). X-ray crystal structures of the two inclusion compounds are reported. Crystals of1·1-PrOH (2: 1) show triclinic (\(P\bar 1\)) symmetry with the unit cell dimensionsa = 10.160(1),b = 14.050(2),c = 15.167(1) Aα = 100.37(1),β = 104.40(1), andγ =94.82(1)°. Crystals of1s·t-BuOH (1: 1) are monoclinic (P21/n) with the cell dimensionsa = 10.603(5),b = 14.377(4),c = 15.664(7) A,β = 104.24(4)°. In both structures, H-bonded loops involving host −000H functions and guest −OH groups establish the supramolecular association. They relate these coordinatoclathrates to previous alcohol inclusions of1. Due to the unusual 2:1 (host: guest) stoichiometry, additional dimer-like interactions between −000H groups of host molecules are found in the 1-PrOH inclusion compound. From the point of view of topology these structures can be referred to as channel inclusion compounds.

The categorical topology approach to fuzzy topology and fuzzy convergence

Abstract It is the purpose of this paper to have a look at fuzzy topology from the point of view of categorical topology. We first look at interesting subcategories of FTS and determine whether they are bireflective and/or coreflective. We also describe the set of all subcategories of FTS which are at the same time bireflective and coreflective. Due to the fact that TOP is one of these subcategories of FTS, FTS itself can be neither Cartesian closed nor extensional. We therefore, secondly, construct a supercategory of FTS which is a topological quasitopos. The construction of this quasitopos is based on the theory of convergence in FTS.

Multihoming in computer networks: A topology-design approach

Multihoming in networks, i.e., attaching a subscriber to more than a single access point in the network, is a mechanism used to increase several performance criteria. In this paper we take the topological design view and address the problem of finding optimal multihoming configurations for several topological design criteria. We analyze the problem and demonstrate that except for dual homing, multihoming is algorithmically complex. Optimal algorithms based on maximum matching in graphs and 0–1 integer programming are given for all cases.

Event driven topology broadcast without sequence numbers

An algorithm is presented that allows each node in a computer network to maintain a correct view of the network topology despite link and node failures. Reliability is achieved without transmitting any information other than the operational status of links. Messages are only sent in response to topological changes: periodic retransmission is not required. >

Towards a topological view of databases

The structure of data constraint which is a major issue to solve database design problems is formally defined as a binary relation over the topology in a finite topological space. we derived deduction procedures based on topological model to solve formally given database design problems. From this topological view, representation for keys and time complexity measure for database design problems are introduced. With a formal definition for key related database design problems which are intractable, the Borel representation for keys classifies the category of database design problems. Under this classification, we identify Borel density as a time complexity measure for formally given database design problems.

Zeeman-Göbel Topologies

In 1967 E. C. Zeeman argued that the Euclidean (i. e. manifold) topology of Minkowski space-time should be replaced by a strictly finer topology that was to have a closer connection with the indefinite metric. This proposal was extended in 1976 by Rudiger Göbel and Hawking, King and McCarthy to the space-times of General Relativity. It is the purpose of this paper to argue that these suggestions for replacement misrepresent the significance of the manifold topology and overstate the necessity for a finer topology. The motivation behind such arguments is a realist view of space-time topology as against (what can be construed to be) the instrumentalist position underlying some of the suggestions for replacement

Functional Organization in the Nucleus

Publisher Summary This chapter integrates the current understanding of the major nuclear functions (replication of DNA, transcription of RNA, transport of RNA and other macromolecules, and formation of mitotic chromosomes) into the framework of the ultrastructural organization of the nucleus, to provide a topological view of nuclear activities. The chapter emphasizes some areas where newer ultrastructural cytochemical methods, such as the localization of specific proteins and nucleic acid sequences by immunocytochemical and in situ hybridization methods, could be applied. The rapid recent advances in the understanding of the structure and functions of chromatin, the structural organization of genes, and transcription have left many areas of nuclear structure and activity unexplored. The characterization of structural elements responsible for the organization of DNA in interphase and in mitotic chromosomes, the location of gene and control sequences with respect to these elements, and the mechanisms of attachment of DNA are among the challenging areas for future research.

Shorter Notes: Totally Geodesic Foliations on 3-Manifolds

If M is a compact 3-manifold, it is known that M can be foliated by 2-manifolds. Topological obstructions are given to the geodesibility of such a foliation IF; that is, to the existence of a Riemannian metric on M making each leaf a totally geodesic submanifold. For example, wil(M) must be infinite, and hence the Reeb foliation of S3 is not geodesible. The study of foliations from the point of view of differential topology has made tremendous progress in recent years; the excellent survey article by Lawson [3] describes many of the most fruitful areas of research. Foliations are also of fundamental importance in differential geometry, particularly in the study of fiber bundles and connections, but the geometric aspects of foliations per se have received considerably less attention. This note considers a geometrization of these topological structures, namely totally geodesic foliations. That is, all leaves are required to be totally geodesic submanifolds. Such foliations arise naturally in Riemannian submersions [51; also, a flat connection on a principal bundle yields a totally geodesic foliation for a suitable metric on the total space [2]. Two basic questions in this realm are: Q1: Given a Riemannian manifold M, does it admit a totally geodesic foliation of a given codimension? Q2: Given a foliation 1Y on a manifold M, is there a Riemannian metric on M such that IF is totally geodesic; namely is '5Y geodesible? If the dimension of ff is one, H. Gluck has recently made significant inroads into these questions [1]. In particular, Gluck has shown that any closed orientable 3-manifold has a geodesic flow, and has characterized those flows on 2-manifolds that are geodesible. However, we show below that the codimension-one case is considerably more restrictive. THEOREM 1. If M is a compact 3-manifold that admits a codimension-one totally geodesic foliation for some Riemannian metric on M, then ir,(M) is infinite. As a particularly interesting special case: COROLLARY. The Reeb foliation of S3 is not geodesible. Received by the editors October 9, 1978 and, in revised form, December 30, 1978. AMS (MOS) subject classifications (1970). Primary 57D30; Secondary 53B25, 53C20.

A view of texture topology and texture description

Problems in texture analysis have become critically important to investigators in the various fields of picture processing because almost all natural surfaces are characterized by local intensity variations. The main problems in texture analysis tire texture discrimination, texture description, and the location of boundaries between regions of different textures. There is no coherent performance theory that subsumes these problems into a general approach, and much previous work has been guided by intuition and pragmatics. In this paper we present a structural hypothesis about textures that are describable as recursively nested intensity regions. Transformations are suggested that map surface structures into higher level structures that reflect deep structures of the textures. It is argued that gray level peaks should he used as textural primitives upon which recursion is based, and the use of several basic peak attributes is proposed for purposes of description. Experimental evidence is given in support of the use of these textural primitives and their attributes, and it is shown how these primitives are competed using the technique of relational trees.

A topological view of P-spaces

A T 1 space in which the intersection or any countably many open sets is open, is called a P-space. In the present paper some basic topological properties of these spaces are studied. Three main results are a characterization of regular paracompact P-spaces, a product theorem for realcompact P-spaces and an example of a Hausdorff connected P-space.

Conserved Particle Structures in General Relativity

When general relativity is examined from the point of view of algebraic topology, it is found that the theory exhibits conserved particlelike structures. The number of such particles associated with a given metric is determined by the homotopy class of the metric. This paper is concerned with showing that if the theory is quantized, then the quantum mechanical states corresponding to 1-particle systems in the unquantized theory may have properties similar to fermions. In particular, it is proved that it is possible for wavefunctionals to exist which are double-valued under 2π rotation.

On non-linear realizations of the groupS U(2)

The non-linear realizations of compact connected Lie groups are considered mainly from the point of view of algebraic topology. In particular, all homogeneous spaces of the groupS U(2) are listed, the construction of a few non-linear realizations ofS U(2) is given and the orbit structure of linear and non-linear realizations are discussed.

Theoretical Analysis of Interchange Composition

Theoretical analysis of interchange composition develops a method of classification of interchange patterns. Patterns are classified according to ramp arrangement in the topological view that difference of patterns depends only upon the difference of ramp arrangement, not on the characteristics of ramp alignment. Illustrations of 193 patterns are presented and their application and evaluation described.

Analysis of product Design in Topological view

Analysis of product Design in Topological view

ON THE TOPOLOGY OF THE GENETIC FINE STRUCTURE

From the classical researches of Morgan and his school [1], the chromosome is known as a linear arrangement of hereditary elements, the genes. These elements must have an internal structure of their own. At this finer level, within the gene the question arises again: what is the arrangement of the sub-elements? Specifically, are they linked together in a linear order analogous to the higher level of integration of the genes in the chromosome? Until recently, the sensitivity of genetic analysis has been insufficient to answer this question. Mapping of a genetic structure is done by observing the recombination of its parts, and recombination involving parts of the structure that are very close together is a rare event. Observation of such rare events requires very many offspring and a selective trick for detecting the few individuals in which the event is recorded. It is for this reason that microorganism are the material of choice for studies of genetic fine structure, and have made it feasible to extend the fineness of genetic mapping by orders of magnitude. In favorable systems, the attainable resolution reaches the level of the molecular subunits of the hereditary material. and experimental testing of the linear arrangement of the finest structural details is therefore possible. A number of cases have been investigated on this level [2]. As a rule, closely linked mutations affecting the same characteristic can be seriated in an unambiguous way, suggesting a linear model. However, the (i.e., recombination frequencies) between mutations are not always strictly additive, and certain complexities (negative interference effects [3,4]) make quantitative analysis difficult. As pointed out by Muller [5] in regard to similar difficulties encountered in mapping on the chromosomal level, strict additivity of should not be taken as the criterion for the linear character of an array. A crucial examination of the question should be made from the point of view of topology, since it is a matter of how the parts of the structure are connected to each other, rather than of the distances between them. Experiments to explore the topology should ask qualitative questions (e.g., do two parts of the structure touch each other or not?) rather than quantitative ones (how far apart are they?). In what follows, such an investigation is attempted for a small portion of the genetic structure of a virus, the rII region of phage T4. Using only qualitative tests, an examination is made of the topology of this structure at the molecular level.