Knots with infinitely many incompressible Seifert surfaces

We show that a knot in $S^3$ with an infinite number of distinct incompressible Seifert surfaces contains a closed incompressible surface in its complement.Comment: 16 pages, 6 figure

Environmental aspects of tensile membrane enclosed spaces

Buildings enclosed by fabric membranes are very sensitive to changes in environmental conditions as a result of their low mass and low thermal insulation values. Development in material technology and the understanding of the structural behaviour of tensile membrane structures along with the vast progress in computer formfinding software, has made it possible for structural design of tensile membrane structures to be approached with almost total confidence. On the contrary, understanding of the environmental behaviour in the spaces enclosed by fabric membrane and their thermal performance is still in its infancy, which to some extent has hindered their wide acceptance by the building industry. The environmental behaviour of tensile membrane structures is outlined and the possible use of the fabric’s topology and geometry particularly to enhance ventilation rates and airflow velocities within the enclosed space is discussed. A need for further research in this area is identified in order to fully realise the potential benefits offered by these structures

Use of fabric membrane topology as an intermediate environment modifier

This paper describes the pattern of airflow around membrane structures, and how they along with the form of the structure itself affect the ventilation rates within their enclosures or their immediate vicinity. Examples that have successfully used membrane skins in the built environment will be reviewed. The possible use of tensile membrane structures topology and orientation to enhance ventilation rates and natural cooling within the semi-enclosed spaces will be discussed. The use of the indigenous fabric skin to tackle key climatic concerns in a simple, elegant manner is discussed along with the review of the wind tunnel experimental visualisation and measurements carried out by the author. These structures go beyond simply providing shading to illustrate innovative, environmentally friendly fabric Architecture, but if properly understood the fabric’s form and topology can play an effective role in the ventilation and natural cooling of spaces in their immediate vicinity

Asymptotics of multivariate sequences, II: multiple points of the singular variety

We consider a multivariate generating function F(z), whose coefficients are indexed by d-tuples of nonnegative integers: F(z) = sum_r a_r z^r where z^r denotes the product of z_j^{r_j} over j = 1, ..., d. Suppose that F(z) is meromorphic in some neighborhood of the origin in complex d-space. Let V be the set where the denominator of F vanishes. Effective asymptotic expansions for the coefficients can be obtained by complex contour integration near points of V. In the first article in this series, we treated the case of smooth points of V. In this article we deal with multiple points of V. Our results show that the central limit (Ornstein-Zernike) behavior typical of the smooth case does not hold in the multiple point case. For example, when V has a multiple point singularity at the point (1, ..., 1), rather than a_r decaying on the order of |r|^{-1/2} as |r| goes to infinity, a_r is a polynomial plus a rapidly decaying term

Environmental performance of spaces enclosed or semi-enclosed by fabric membrane structures

. Since the 1960s a large evolution took place in the fabric structures industry, as they became more complex with time, and designers have been able to keep up with the structural implications of this changing situation. Sophisticated analytical models and computer software have facilitated the structural design of tensile membrane structures (TMS) and this has produced a diverse and complex range of design and form solutions. However, environmental issues continue to be dealt with in a cursory manner, which is still today unable to fully satisfy the client’s requirements. With the vast interest in these structures, designers and manufacturers alike realised that if membrane enclosed spaces is to compete with other more conventional enclosures, a clear understanding of their environmental behaviour should be available to them. Moreover that if membrane enclosed spaces were to aspire to the same level of environmental performance as more conventional buildings, it would be necessary to develop tailored analytical techniques, which could be used to assess the likely performance of various design alternatives. This paper explores the thermal performance of membrane structures, and how these structures can be used as climate modifiers in spaces enclosed or semi enclosed by fabric membrane skins, providing thermal comfort for the occupiers. Analytical techniques that are used to investigate the environmental behaviour of fabric membranes and assessing their liability will be reviewed. The paper also looks at some of the work done by other researchers in the investigation of the thermal behaviour of fabric membranes by different techniques