Topic

# Plane (geometry)

About: Plane (geometry) is a research topic. Over the lifetime, 39375 publications have been published within this topic receiving 494447 citations.

##### Papers published on a yearly basis

##### Papers

More filters

••

TL;DR: In this article, the absorption index at the wave length of the band maximum was found to be proportional to the total concentration of metal at shorter wave lengths, however, deviations were observed, the absorption increasing more rapidly with concentration than Beers' law would demand.

Abstract: solutions investigated, the absorption index diminishing approximately 1% for a rise in temperature of one degree. 6. In liquid ammonia rough measurements of concentration showed the absorption index to be proportional to the total concentration of metal. 7. In methylamine the absorption index, at the wave length of the band maximum is also proportional to the total concentration of metal. At shorter wave lengths, however, deviations were observed, the absorption increasing more rapidly with concentration than Beers’ law would demand. The ratio of the absorption index a t 650pp to that a t 53opp increases not only with increasing concentration of the metal but also with increasing concentration of the reaction product of the metal with methylamine, and probably also with increasing temperature. 8. These observations can be accounted for by the following hypotheses: The color in all cases is due to electrons combined with the solvent. In ammonia the dissociation of the metal into electrons is nearly complete, and the concentration of electrons uncombine4 with solvent is negligible compared with that of the solvated electrons. In other words, the solvation of the electrons is nearly complete. In methylamine, on the other hand, the concentration of un-ionized metal is no longer negligible and is responsible for the increased absorption a t the shorter wave lengths. The solvation of the electrons in methylamine is incomplete and diminishes as the temperature is increased.

18,573 citations

01 Jan 1985

TL;DR: This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry.

Abstract: From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry...The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two."

6,525 citations

••

TL;DR: In this article, a general, numerical, marching procedure is presented for the calculation of the transport processes in three-dimensional flows characterised by the presence of one coordinate in which physical influences are exerted in only one direction.

Abstract: A general, numerical, marching procedure is presented for the calculation of the transport processes in three-dimensional flows characterised by the presence of one coordinate in which physical influences are exerted in only one direction. Such flows give rise to parabolic differential equations and so can be called three-dimensional parabolic flows. The procedure can be regarded as a boundary-layer method, provided it is recognised that, unlike earlier published methods with this name, it takes full account of the cross-stream diffusion of momentum, etc., and of the pressure variation in the cross-stream plane. The pressure field is determined by: first calculating an intermediate velocity field based on an estimated pressure field; and then obtaining appropriate correction so as to satisfy the continuity equation. To illustrate the procedure, calculations are presented for the developing laminar flow and heat transfer in a square duct with a laterally-moving wall.

5,946 citations

•

TL;DR: In this article, a convolution-backprojection formula is deduced for direct reconstruction of a three-dimensional density function from a set of two-dimensional projections, which has useful properties, including errors that are relatively small in many practical instances and a form that leads to convenient computation.

Abstract: A convolution-backprojection formula is deduced for direct reconstruction of a three-dimensional density function from a set of two-dimensional projections. The formula is approximate but has useful properties, including errors that are relatively small in many practical instances and a form that leads to convenient computation. It reduces to the standard fan-beam formula in the plane that is perpendicular to the axis of rotation and contains the point source. The algorithm is applied to a mathematical phantom as an example of its performance.

5,356 citations

••

TL;DR: In this article, a convolution-backprojection formula is deduced for direct reconstruction of a three-dimensional density function from a set of two-dimensional projections, which has useful properties, including errors that are relatively small in many practical instances and a form that leads to convenient computation.

Abstract: A convolution-backprojection formula is deduced for direct reconstruction of a three-dimensional density function from a set of two-dimensional projections. The formula is approximate but has useful properties, including errors that are relatively small in many practical instances and a form that leads to convenient computation. It reduces to the standard fan-beam formula in the plane that is perpendicular to the axis of rotation and contains the point source. The algorithm is applied to a mathematical phantom as an example of its performance.

5,329 citations