This paper presents a graphical procedure for the squaring of a circle of any radius. This procedure, which is based on a novel application of the involute profile, when applied to a circle of arbitrary radius (using ...This paper presents a graphical procedure for the squaring of a circle of any radius. This procedure, which is based on a novel application of the involute profile, when applied to a circle of arbitrary radius (using only an unmarked ruler and a compass), produced a square equal in area to the given circle, which is 50 cm<sup>2</sup>. This result was a clear demonstration that not only is the construction valid for the squaring of a circle of any radius, but it is also capable of achieving absolute results (independent of the number pi (π), in a finite number of steps), when carried out with precision.展开更多
This paper presents a Method for the squaring of a circle (i.e., constructing a square having an area equal to that of a given circle). The construction, when applied to a given circle having an area of 12.7 cm<sup...This paper presents a Method for the squaring of a circle (i.e., constructing a square having an area equal to that of a given circle). The construction, when applied to a given circle having an area of 12.7 cm<sup>2</sup>, it produced a square having an area of 12.7 cm<sup>2</sup>, using only an unmarked ruler and a compass. This result was a clear demonstration that not only is the construction valid for the squaring of a circle but also for achieving absolute results (independent of the number pi (π) and in a finite number of steps) when carried out with precision.展开更多
In this paper, we study resource management models and algorithms that satisfy multiple performance objects simultaneously. We realize the proportional fairness principle based QoS model, which defines both delay and ...In this paper, we study resource management models and algorithms that satisfy multiple performance objects simultaneously. We realize the proportional fairness principle based QoS model, which defines both delay and loss rate requirements of a class, to include fairness, which is important for the integration of multiple service classes. The resulting Proportional Fairness Scheduling model formalizes the goals of the network performance, user’s QoS requirement and system fairness and exposes the fundamental tradeoffs between these goals. In particular, it is difficult to simultaneously provide these objects. We propose a novel scheduling algorithm called Proportional Fairness Scheduling (PFS) that approximates the model closely and efficiently. We have implemented the PFS scheduling in Linux. By performing simulation and measurement experiments, we evaluate the delay and loss rate proportional fairness of PFS, and determine the computation overhead.展开更多
文摘This paper presents a graphical procedure for the squaring of a circle of any radius. This procedure, which is based on a novel application of the involute profile, when applied to a circle of arbitrary radius (using only an unmarked ruler and a compass), produced a square equal in area to the given circle, which is 50 cm<sup>2</sup>. This result was a clear demonstration that not only is the construction valid for the squaring of a circle of any radius, but it is also capable of achieving absolute results (independent of the number pi (π), in a finite number of steps), when carried out with precision.
文摘This paper presents a Method for the squaring of a circle (i.e., constructing a square having an area equal to that of a given circle). The construction, when applied to a given circle having an area of 12.7 cm<sup>2</sup>, it produced a square having an area of 12.7 cm<sup>2</sup>, using only an unmarked ruler and a compass. This result was a clear demonstration that not only is the construction valid for the squaring of a circle but also for achieving absolute results (independent of the number pi (π) and in a finite number of steps) when carried out with precision.
基金supported by the National Natural Science Foundation of China(Grant Nos.90104002,69725003)
文摘In this paper, we study resource management models and algorithms that satisfy multiple performance objects simultaneously. We realize the proportional fairness principle based QoS model, which defines both delay and loss rate requirements of a class, to include fairness, which is important for the integration of multiple service classes. The resulting Proportional Fairness Scheduling model formalizes the goals of the network performance, user’s QoS requirement and system fairness and exposes the fundamental tradeoffs between these goals. In particular, it is difficult to simultaneously provide these objects. We propose a novel scheduling algorithm called Proportional Fairness Scheduling (PFS) that approximates the model closely and efficiently. We have implemented the PFS scheduling in Linux. By performing simulation and measurement experiments, we evaluate the delay and loss rate proportional fairness of PFS, and determine the computation overhead.
