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We construct and investigate the high-order symmetric explicit and implicit methods to solve the systems of second-order ordinary differential equations. The methods were selected according to size of the interval of periodicity, an error constant, behaviour of the roots of the stability polynomial, and accuracy of numerical solution of tests problem including simulation of disturbed orbital motion.

Background The aim of this study was to evaluate the comparative precision and accuracy of multiple methods of thermometry used to assess body temperature in healthy adult ferrets. Methods Temperature was measured in 20 healthy ferrets (Mustela putorius furo) using noncontact infrared thermometry, digital thermometry in the rectal, inguinal, and axillary regions, and infrared contact-based thermometer in the ear (tympanic) and on the skin of the dorsal back between the shoulder blades. Temperatures were taken pre- and posthandling, evaluated across the set of ferrets for general precision and effect of handling, and compared to assess accuracy. Intraclass correlation analysis and Bland-Altman agreement analyses with rectal temperature being used as reference were conducted. Results Sample time (before and after physical examination) and day (day #1 and day #2), were found to not to be significantly different with respect to temperature measurements (P > 0.05). Reproducibility was not high for any of the temperature measurement methods, but was moderate for rectal and tympanic ear measures. The lowest mean difference with rectal temperature was found for tympanic thermometry on the dorsal skin when compared with rectal measurement (+0.05° C), as opposed to the other four methods of temperature measurement which ranged in their mean differences when compared with rectal measurement (−7.4 to −0.58° C). Agreement analyses showed constant error and proportional error only for the inguinal temperature method. Conclusions and clinical relevance Temperature measurements due to tympanic thermometers applied on the dorsal skin have some agreement with respect to digital rectal thermometry in ferrets. Following further validating studies on hypothermic and hyperthermic contexts of usage, this less invasive approach may be a useful method for temperature measurement in clinical settings to reduce stress of the patient and increase efficiency without sacrificing accuracy.

Implicit Runge- Kutta methods are used for solving stiff problems which mostly arise in real life situations. Analysis of the order, error constant, consistency and convergence will help in determining an effective Runge- Kutta Method (RKM) to use. Due to the loss of linearity in Runge –Kutta Methods and the fact that the general Runge –Kutta Method makes no mention of the differential equation makes it impossible to define the order of the method independently of the differential equation. In this paper, we examine in simpler details how to obtain the order, error constant, consistency and convergence of a Runge -Kutta Type method (RKTM) when the step number .

Purpose: We investigated the perception of affordances for vertical jumping-and-reaching and horizontal jumping by children. Method: In the horizontal task, children were asked to judge their ability in the standing long jump. In the vertical task, children were asked to judge the height of a ball that they could run to, jump up, and reach with their fingertips. Following judgments, children performed both types of jumps. We compared gymnasts (children with at least 2 years of gymnastics training; 7.92 ± 0.91 years) versus children with no competitive athletic experience (7.74 ± 0.86 years). Results: As expected, actual ability was greater in gymnasts than in non-athletes, for both types of jump (each p < .001). We separately analyzed Constant Error and Absolute Error of judgments (relative to actual performance). Results revealed that gymnasts tended toward underestimation, while non-athletes tended toward overestimation. Absolute error differed between tasks for the non-athletes (p < .001), but for the gymnasts the difference between conditions was not significant (p = .25). Absolute error differed between groups for vertical jump-and-reach (p < .01) but not for horizonal jump (p = .17). Conclusions: Gymnastics experience was associated with a generalized tendency for children to underestimate their jumping ability. In addition, gymnastics experience was associated with judgment accuracy that was consistent across tasks. The results reveal that gymnastics training is associated with changes in athletic ability, but also with changes in the perception of affordances.

The obtained generalized mathematical model of micromechanical and rotary vibrating gyroscopes as meters of angular velocity and transfer functions of meters. The features of the dynamics of vibration gyros according to the generalized model and their influence on the properties of the transfer function of the angular velocity meter are determined. The properties of the constant error and the trend of the output signal of micromechanical gyroscopes are investigated.

Body mass index (BMI)-based body fat equations from Womersley (BMIWOMERSLEY), Jackson (BMIJACKSON), Deurenberg (BMIDEURENBERG), and Gallagher (BMIGALLAGHER) are practical in clinical and field settings. However, research has shown these prediction equations produce large error, which may be due to the inability of BMI to account for differences in fat mass and fat-free mass. Thus, accounting for variations in muscular strength via relative handgrip (RHG) strength could help enhance the accuracy of a BMI-based body fat equation. Purpose The purpose of the current study was twofold: 1) to develop a new BMI-based body fat equation that includes the measurement of RHG (BMINICKERSON) and 2) to cross-validate BMINICKERSON, BMIWOMERSLEY, BMIJACKSON, BMIDEURENBERG, and BMIGALLAGHER against a four-compartment criterion. Methods The development and cross-validation samples consisted of 230 and 110 participants, respectively. Criterion body fat percent was determined with a four-compartment model. RHG was calculated by summing the max of each handgrip strength measurement and dividing by body mass. BMI (kg·m), RHG (kg·kg), age (yr), ethnicity (Hispanic or non-Hispanic White), and sex (male or female) were entered into a stepwise regression to calculate BMINICKERSON. Results BMINICKERSON was calculated as follows: body fat percent = 21.504 - (12.484 × RHG) - (7.998 × sex) + (0.722 × BMI). In the cross-validation sample, BMINICKERSON produced lower constant error (CE) and total error (TE) values (CE = -0.11%, TE = 4.28%) than all other BMI-based body fat equations (CE = 0.89%-1.90%, TE = 5.71%-6.87%). Furthermore, the 95% limits of agreement were lower for BMINICKERSON ± 8.47% than previous BMI-based body fat equations (95% limits of agreement = ±11.14% to 13.33%). Conclusion Current study results confirm that previous BMI-based body fat equations produce large error in Hispanics and non-Hispanic Whites but can be improved by accounting for RHG. Allied health professionals are encouraged to use BMINICKERSON in clinical and field settings for adiposity assessments.

Estimates of body composition have been derived using 3-dimensional optical imaging (3DO), but no equations to date have been calibrated using a 4-component (4C) model criterion. This investigation reports the development of a novel body fat prediction formula using anthropometric data from 3DO imaging and a 4C model. Anthropometric characteristics and body composition of 179 participants were measured via 3DO (Size Stream® SS20) and a 4C model. Machine learning was used to identify significant anthropometric predictors of body fat (BF%), and stepwise/lasso regression analyses were employed to develop new 3DO-derived BF% prediction equations. The combined equation was externally cross-validated using paired 3DO and DXA assessments (n = 158), producing a R2 value of 0.78 and a constant error of (X ± SD) 0.8 ± 4.5%. 3DO BF% estimates demonstrated equivalence with DXA based on equivalence testing with no proportional bias in the Bland–Altman analysis. Machine learning methods may hold potential for enhancing 3DO-derived BF% estimates.

The purpose of the present study was: (1) to develop a new dual-energy X-ray absorptiometry (DXA)-derived body volume (BV) equation with the GE-Lunar prodigy while utilising underwater weighing (UWW) as a criterion and (2) to cross-validate the novel DXA-derived BV equation (4C-DXANickerson), Wilson DXA-derived BV equation (4C-DXAWilson) and air displacement plethysmography (ADP)-derived BV (4C-ADP) in Hispanic adults. A total of 191 Hispanic adults (18–45 years) participated in the present study. The development sample consisted of 120 females and males (50 % females), whereas the cross-validation sample comprised of forty-one females and thirty males (n 71). Criterion body fat percentage (BF %) and fat-free mass (FFM) were determined using a four-compartment (4C) model with UWW as a criterion for BV (4C-UWW). 4C-DXANickerson, 4C-DXAWilson and 4C-ADP were compared against 4C-UWW in the cross-validation sample. 4C-DXANickerson, 4C-DXAWilson and 4C-ADP all produced similar validity statistics when compared with 4C-UWW in Hispanic males (all P > 0·05). 4C-DXANickerson also yielded similar BF % and FFM values as 4C-UWW when evaluating the mean differences (constant error (CE)) in Hispanic females (CE = –0·79 % and 0·38 kg; P = 0·060 and 0·174, respectively). However, 4C-DXAWilson produced significantly different BF % and FFM values (CE = 3·22 % and –2·20 kg, respectively; both P < 0·001). Additionally, 4C-DXAWilson yielded significant proportional bias when estimating BF % (P < 0·001), whereas 4C-ADP produced significant proportional bias for BF % and FFM (both P < 0·05) when evaluated in Hispanic females. The present study findings demonstrate that 4C-DXANickerson is a valid measure of BV in Hispanics and is recommended for use in clinics, where DXA is the main body composition assessment technique.

The study aimed to investigate the impact of a 12-week strength training program on force accuracy and steadiness changes in lower limbs in young healthy men. Twenty subjects with a dominant right lower limb were included. They performed a force matching task both pre and post strength training program. The ability to reproduce force was determined by calculating three errors: absolute error (AE), constant error (CE), and variable error (VE). After intervention AE and VE improved in both legs indicating higher improvement in the dominant leg (p = 0.032 for AE and p = 0.005 for VE). However, CE improved only in the dominant leg (p = 0.001). We conclude that strength training improved the accuracy and consistency of force in a force reproduction task. This improvement was more evident in the dominant lower limb. Most likely, the inter-limb asymmetry in changes of force application ability caused by strength training is due to the different mechanisms responsible for the control of voluntary movements in the dominant and non-dominant lower limb.

In this paper, we propose $$L^2(J;H^1_0(\Omega ))$$ L 2 ( J ; H 0 1 ( Ω ) ) and $$L^2(J;L^2(\Omega ))$$ L 2 ( J ; L 2 ( Ω ) ) norm error estimates that provide the explicit values of the error constants for the semi-discrete Galerkin approximation of the linear heat equation. The derivation of these error estimates shows the convergence of the approximation to the weak solution of the linear heat equation. Furthermore, explicit values of the error constants for these estimates play an important role in the computer-assisted existential proofs of solutions to semi-linear parabolic partial differential equations. In particular, the constants provided in this paper are better than the existing constants and, in a sense, the best possible.

Understanding the effects of acute feeding on body composition and metabolic measures is essential to the translational component and practical application of measurement and clinical use. To investigate the influence of acute feeding on the validity of dual-energy X-ray absorptiometry (DXA), a four-compartment model (4C) and indirect calorimetry metabolic outcomes, thirty-nine healthy young adults (n 19 females; age: 21·8 (sd 3·1) years, weight; 71·5 (sd 10·0) kg) participated in a randomised cross-over study. Subjects were provided one of four randomised meals on separate occasions (high carbohydrate, high protein, ad libitum or fasted baseline) prior to body composition and metabolic assessments. Regardless of macronutrient content, acute feeding increased DXA percent body fat (%fat) for the total sample and females (average constant error (CE):–0·30 %; total error (TE): 2·34 %), although not significant (P = 0·062); the error in males was minimal (CE: 0·11 %; TE: 0·86 %). DXA fat mass (CE: 0·26 kg; TE: 0·75 kg) and lean mass (LM) (CE: 0·83 kg; TE: 1·23 kg) were not altered beyond measurement error for the total sample. 4C %fat was significantly impacted from all acute feedings (avg CE: 0·46 %; TE: 3·7 %). 4C fat mass (CE: 0·71 kg; TE: 3·38 kg) and fat-free mass (CE: 0·55 kg; TE: 3·05 kg) exceeded measurement error for the total sample. RMR was increased for each feeding condition (TE: 1666·9 kJ/d; 398 kcal/d). Standard pre-testing fasting guidelines may be important when evaluating DXA and 4C %fat, whereas additional DXA variables (fat mass and LM) may not be significantly impacted by an acute meal. Measuring body composition via DXA under less stringent pre-testing guidelines may be valid and increase feasibility of testing in clinical settings.

In this paper, An $$FO-{{I}^{\lambda }}{{D}^{1-\lambda }}$$ controller is proposed for the level control problem in Two Input Two Output-Liquid Level System (TITO-LLS). The proposed $$FO-{{I}^{\lambda }}{{D}^{1-\lambda }}$$ controller is designed based on phase margin ( $${{\phi }_{m}}$$ ), gain crossover frequency ( $${{\omega }_{gc}}$$ ) and velocity error constant ( $${{K}_{v}}$$ ) specifications. Oustaloup Recursive Approximation (ORA) method is used to realize the velocity error constant. A mathematical procedure is proposed to identify the linear dynamics of TITO-LLS from the real-time response. An inverted decoupler is used to decouple the TITO-LLS into two separate Single Input Single Output (SISO) systems. The effectiveness of the proposed controller is compared with reported works both in simulation and in real-time. It is observed that the proposed controller gives better results than the existing reported works.

This article describes an algorithm in a smartphone designed to support the accuracy test, periodically done by network operators in energy meters. The algorithm is implemented in a mobile application with the IDE Android Studio. The applied methodology implies in the first stage video stabilization, in the second stage a novel method for the rejection of noise by illumination changes, and in the third stage the estimation of the percentual error of an electromechanical meter. The results of the application show a standard deviation of 0.1354 s, lower than the standard deviation of the manual method = 0.1966 s, which indicates a good performance of the mobile application. The experiment performed show 95% of the accuracy tests performed match the result with those performed manually

A reduced capacity to generate and sustain cervical muscle force over a range of contraction intensities is a feature of some participants with neck pain. To date there have been no studies comparing the accuracy of force perception in participants with and without neck pain.Cross-sectional observational study.Participants with (n = 25) and without (n = 25) neck pain performed isometric muscle contractions at three progressive self-perceived (no feedback provided) intensities (10, 25, 50) % of their maximal voluntary contraction (MVC) in cervical: flexion, extension, right and left lateral flexion. Absolute error (AE), constant error (CE), and variable error (VE) between actual and targeted force values were calculated.The neck pain group had: (1) AE-combined direction -significantly higher at 10% and lower at 50% (p 0.05); (2) significantly lower CE in most measures (p 0.05); (3) higher mean VE in all measures, with 10, 25, and 50% combined direction and overall combined % extension significantly higher (p 0.05).Findings indicate higher variability in force generation perception across all directions and intensities in participants with neck pain compared to healthy controls. Potentially this greater variability might suggest impaired force sense, a construct of proprioception in participants with neck pain. Reduced force sense may have implications for participants with neck pain during functional activities requiring precision and may need to be trained. Further research is required.

In this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly supported window function. Here, we consider the continuous Kaiser–Bessel, continuous exp-type, sinh-type, and continuous cosh-type window functions with the same support and same shape parameter. We present novel explicit error estimates for NFFT with such a window function and derive rules for the optimal choice of the parameters involved in NFFT. The error constant of a window function depends mainly on the oversampling factor and the truncation parameter. For the considered continuous window functions, the error constants have an exponential decay with respect to the truncation parameter.