Squaring Rectangles for Dumbbells

نویسنده

  • J. W. CANNON
چکیده

The theorem on squaring a rectangle (see Schramm [6] and CannonFloyd-Parry [1]) gives a combinatorial version of the Riemann mapping theorem. We elucidate by example (the dumbbell) some of the limitations of rectangle-squaring as an approximation to the classical Riemamnn mapping.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Random Infinite Squarings of Rectangles

A recent publication [1] introduced a growth procedure for planar maps, whose almost sure limit is “the uniform infinite 3-connected planar map”. A classical construction of Brooks, Smith, Stone and Tutte [7] associates a squaring of a rectangle (i.e. a tiling of a rectangle by squares) to any finite, edge-rooted planar map with nonseparating root edge. We use this construction together with th...

متن کامل

Directed orientation of asymmetric composite dumbbells by electric field induced assembly.

Assembly and directed orientation of anisotropic particles with an external ac electric field in a range from 1 kHz to 2 MHz were studied for asymmetric composite dumbbells incorporating a silica, titania, or titania/silica (titania:silica = 75:25 vol %) sphere. The asymmetric composite dumbbells, which were composed of a polymethylmethacrylate (PMMA)-coated sphere (core-shell part) and a polys...

متن کامل

Sequence-independent inhibition of RNA transcription by DNA dumbbells and other decoys.

DNA dumbbells are stable, short segments of double-stranded DNA with closed nucleotide loops on each end, conferring resistance to exonucleases. Dumbbells may be designed to interact with transcription factors in a sequence-specific manner. The internal based paired sequence of DNA dumbbells in this study contains the X-box, a positive regulatory motif found in all MHC class II DRA promoters. I...

متن کامل

A THEORETICALLY CORRECT RESOURCE USAGE VISUALIZATION FOR THE RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM

The cumulative resource constraints of the resource-constrained project scheduling problem (RCPSP) do not treat the resource demands as geometric rectangles, that is, activities are not necessarily assigned to the same resource units over their processing times. In spite of this fact, most papers on resource-constrained project scheduling mainly in the motivation phase use a strip packing of re...

متن کامل

Squaring and Not Squaring One or More Planes

A set of natural numbers tiles the plane if a square-tiling of the plane exists using exactly one square of sidelength n for every n in the set. In [9] it is shown that N, the set of all natural numbers, tiles the plane. We answer here a number of questions from that paper. We show that there is a simple tiling of the plane (no nontrivial subset of squares forms a rectangle). We show that neith...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008