Dear Experts, I asked about a turning identification last few weeks. I got much help from the list and was really really happy. When part of the work was published, I was happy to show you and further thank the contributors. Unfortunately, the moderator didn't allow the pdf to go. A link was rather recommended. I am putting the link here for you. Thank you very much. The work I do using R is acceptable in some high impact journals. Best regards Ogbos Abstract: https://academic.oup.com/mnras/article-abstract/493/2/1948/5764172 Article (free access): https://academic.oup.com/mnras/article/493/2/1948/5764172?guestAccessKey=ce6965a5-a228-4b9a-b544-128953e05f17