ARTICLE | doi:10.20944/preprints201902.0243.v1
Subject: Computer Science And Mathematics, Applied Mathematics Keywords: Convex function, Ostrowski inequality, Holder's inequality, Power mean inequality, Conformable integrals, Midpoint formula
Online: 26 February 2019 (13:10:40 CET)
In the article, by applied the concept of strongly convex function and one known identity, we establish several Ostrowski type inequalities involving conformable fractional integrals. As applications, some new error estimations for the midpoint formula are provided as well.
ARTICLE | doi:10.20944/preprints201803.0017.v1
Subject: Computer Science And Mathematics, Analysis Keywords: Finite Hilbert Transform; Lipschitzian; Monotonic; Convex functions; Midpoint and Trapezoid inequalities; Ostrowski's inequality; Taylor's formula
Online: 2 March 2018 (05:11:07 CET)
In this paper we survey some recent results due to the author concerning various inequalities and approximations for the finite Hilbert transform of a function belonging to several classes of functions, such as: Lipschitzian, monotonic, convex or with the derivative of bounded variation or absolutely continuous. More accurate estimates in the case that the higher order derivatives are absolutely continuous, are also provided. Some quadrature rules with error bounds are derived. They can be used in the numerical integration of the finite Hilbert transform and, due to the explicit form of the error bounds, enable the user to predict a priory the accuracy.
ARTICLE | doi:10.20944/preprints202306.1826.v1
Subject: Public Health And Healthcare, Public Health And Health Services Keywords: midpoint of sleep; eating events; meals; obesity; schoolchildren; bedtime
Online: 26 June 2023 (14:27:32 CEST)
Sleep timing is one of the dimensions of sleep that refers to the time of day when sleep occurs. It was included in sleep-related research because of the potential associations between overweight and consumption of meals and snacks. This cross-sectional study aimed to investigate associations between sleep timing, meal and snack consumption, and weight status in 1333 schoolchildren aged 7-14 years. The midpoint of sleep was used as a sleep timing measure obtained by the midpoint between bedtime and wake-up time and classify as Early, intermediate, and Late. Schoolchildren in the Early group were less likely to be overweight (OR: 0.83, 95% CI 0.69; 0.99), had higher odds of mid-morning snack consumption (OR: 1.95, 95%CI 1.56; 2.44) and lower probability to consume the evening snack (OR: 0.75, 95%CI 0.59; 0.94) compared with the Intermediate group. The Late group had lower odds of mid-morning snack consumption (OR: 0.67, 95%CI 0.55, 0.80) than the Intermediate group. The consumption of mid-morning and evening snacks was associated with the Early and the Late midpoint of sleep. These results suggest that bedtime and wake-up time are relevant to consuming meals and snacks and may also be related to a greater probability of being overweight in children and adolescents.
ARTICLE | doi:10.20944/preprints202302.0082.v1
Subject: Computer Science And Mathematics, Applied Mathematics Keywords: arctangent function; midpoint integration; iterative algorithm; constant pi
Online: 6 February 2023 (07:11:07 CET)
In this work we derive a generalized series expansion of the acrtangent function by using the enhanced midpoint integration (EMI). Algorithmic implementation of the generalized series expansion utilizes a simple two-step iteration. This approach significantly improves the convergence and requires no surd numbers in computation of the arctangent function.
ARTICLE | doi:10.20944/preprints202107.0254.v1
Subject: Engineering, Automotive Engineering Keywords: robot path planning; RRT; midpoint interpolation; triangular rewiring; path smoothness
Online: 12 July 2021 (12:05:01 CEST)
To solve the problem that sampling-based Rapidly-exploring Random Tree (RRT) method is difficult to guarantee optimality. This paper proposed the Post Triangular Processing of Midpoint Interpolation method minimized the planning time and shorter path length of the sampling-based algorithm. The proposed Post Triangular Processing of Midpoint Interpolation method makes a closer to the optimal path and somewhat solves the sharp path problem through the interpolation process. The experiments were conducted to verify the performance of the proposed method. Applying the method proposed in this paper to the RRT algorithm increases the efficiency of optimization compared to the planning time.