The ultimate goal in studying sequences, and the most frequently appearing theme in university entrance exams, is "recurrence relations" and "mathematical induction." A recurrence relation defines the ...

In this article, as an introduction to Part IX, we will summarize the overall approach of "finding expected values using recurrence relations." Recurrence relations are a powerful weapon for problems ...

Monitored quantum dynamics underpin emerging quantum technologies. This work shows that, in many-body systems, recurrence time—the duration required for the initial state to be first detected again—is ...

1 Child and Adolescent Forensic Mental Health Service, Oxford, UK 2 Section of Child and Adolescent Psychiatry, University of Oxford, Warneford Hospital, Oxford, UK Background: Children who have been ...

Abstract: This paper presents a robust method for 3D object rotation estimation using spherical harmonics representation and the unit quaternion vector. The proposed method provides a closed-form ...

Background Diagnosis of a child with a genetic condition leads to parents asking whether there is a risk the condition could occur again with future pregnancies. If the cause is identified as an ...

Ukraine’s anti-corruption agency has accused a former energy minister of laundering millions of dollars. German Galushchenko, who led the department from 2021 until 2025, was detained by border guards ...

SINGAPORE – Early investigations found that the root cause of the recent bus arrival timing issues was a software defect on the buses, triggered by a server failure in January, Acting Transport ...

Objective To examine the association between dietary patterns and colorectal cancer (CRC) survival. Design Cohort study. Setting A familial CRC registry in Newfoundland. Participants 529 newly ...

Abstract: In order to derive the linear relations for solving the singular matrix problem during the recurrence process of the precise integration time-domain method, an electromagnetic closed-surface ...

33% reduction in relative risk of invasive disease observed in pre-menopausal early breast cancer (EBC) patients receiving Kisqali in 1-year post-treatment analysis 1 Tolerability remained consistent, ...