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Article
Publication date: 12 August 2021

Mustafa Bojakli and Hasan Sankari

The authors have determined whether the points fixed by all the full and the partial Atkin–Lehner involutions WQ on X0(N) for N ≤ 50 are Weierstrass points or not.

Abstract

Purpose

The authors have determined whether the points fixed by all the full and the partial Atkin–Lehner involutions WQ on X0(N) for N ≤ 50 are Weierstrass points or not.

Design/methodology/approach

The design is by using Lawittes's and Schoeneberg's theorems.

Findings

Finding all Weierstrass points on X0(N) fixed by some Atkin–Lehner involutions. Besides, the authors have listed them in a table.

Originality/value

The Weierstrass points have played an important role in algebra. For example, in algebraic number theory, they have been used by Schwartz and Hurwitz to determine the group structure of the automorphism groups of compact Riemann surfaces of genus g ≥ 2. Whereas in algebraic geometric coding theory, if one knows a Weierstrass nongap sequence of a Weierstrass point, then one is able to estimate parameters of codes in a concrete way. Finally, the set of Weierstrass points is useful in studying arithmetic and geometric properties of X0(N).

Details

Arab Journal of Mathematical Sciences, vol. 29 no. 1
Type: Research Article
ISSN: 1319-5166

Keywords

Article
Publication date: 17 May 2011

Shunan Wu, Zhaowei Sun, Gianmarco Radice and Xiande Wu

One of the primary problems in the field of on‐orbit service and space conflict is related to the approach to the target. The development of guidance algorithms is one of the main…

Abstract

Purpose

One of the primary problems in the field of on‐orbit service and space conflict is related to the approach to the target. The development of guidance algorithms is one of the main research areas in this field. The objective of this paper is to address the guidance problem for autonomous proximity manoeuvres of a chase‐spacecraft approaching a target spacecraft.

Design/methodology/approach

The process of autonomous proximity is divided into three phases: proximity manoeuvre, fly‐around manoeuvre, and final approach. The characteristics of the three phases are analyzed. Considering the time factor of autonomous proximity, different orbits for the three phases are planned. Different guidance algorithms, which are based on multi‐pulse manoeuvres, are then devised.

Findings

This paper proposes three phases of autonomous proximity and then designs a guidance method, which hinges on a multi‐pulse algorithm and different orbits for the three phases; in addition, a method of impulse selection is devised.

Practical implications

An easy methodology for the analysis and design of autonomous proximity manoeuvres is proposed, which could also be considered for other space applications such as formation flying deployment and reconfiguration.

Originality/value

Based on this guidance method, the manoeuvre‐flight period of the chase‐spacecraft can be set in accordance with the mission requirements; the constraints on fuel mass and manoeuvre time are both considered and satisfied. Consequently, this proposed guidance method can effectively deal with the problem of proximity approach to a target spacecraft.

Details

Aircraft Engineering and Aerospace Technology, vol. 83 no. 3
Type: Research Article
ISSN: 0002-2667

Keywords

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