Gauss Legendre Quadrature Formulae for Tetrahedra

In this paper we consider the Gauss Legendre quadrature method for numerical integration over the standard tetrahedron: {(x, y, z)| 0 ≤ x, y, z ≤ 1, x + y + z ≤ 1} in the Cartesian three-dimensional (x, y, z) space. The mathematical transformation from the (x, y, z) space to (ξ, η, ζ) space is described to map the standard tetrahedron in (x, y, z) space to a standard 2-cube: {(ξ, η, ζ)| − 1 ≤ ξ, η, ζ ≤ 1} in the (ξ, η, ζ) space. This overcomes the difficulties associated with the derivation of new weight co-efficients and sampling points. The effectiveness of the formulae is demonstrated by applying them to the integration of three nonpolynomial and three polynomial functions

The Use of Parabolic Arc in Matching Curved Boundary by Point Transformations for Sextic Order Triangular Element

Abstract This paper is concerned with curved boundary triangular element having one curved side and two straight sides. The curved element considered here is the 28-node (sextic) triangular element. On using the isoparametric coordinate transformation, the curved triangle in the global ) , ( y x coordinate system is mapped into a standard triangle: { } . Under this transformation curved boundary of this triangular element is implicitly replaced by sextic arc. The equation of this arc involves parameters, which are the coordinates of points on the curved side. This paper deduces relations for choosing the parameters in sextic arc in such a way that each arc is always a parabola which passes through four points of the original curve, thus ensuring a good approximation. The point transformations which are thus determined with the above choice of parameters on the curved boundary and also in turn the other parameters in the interior of curved triangle will serve as a powerful subparametric coordinate transformation for higher order curved triangular elements with one curved side and two straight sides

Genetic evaluation of Kankrej bulls by different sire evaluation methods

The genetic evaluation of Kankrej bulls was done by using three different methods viz., BLUP, Wombat sire, and Wombat animal models. First lactation 305-days yields of 348 daughters born to 9 sires and calved from 2016 to 2020 were used for the analyses. For BLUP analysis, season and year of calving were considered as fixed effects, and sire was considered as random effect. The overall average estimate of 2414.40 kg was obtained in BLUP method while 2430.29 kg was obtained in both Wombat sire and animal models. The results revealed that the Wombat animal model discriminated against the sires to the maximum extent followed by Wombat sire and BLUP models. Based on the results, two Kankrej bulls viz., K.8.32 and K.8.62 can be selected as proven bulls for nominated mating for improving the milk productivity of Kankrej cattle.

The clinical and cost-effectiveness of corticosteroid injection versus night splints for carpal tunnel syndrome (INSTINCTS trial): an open-label, parallel group, randomised controlled trial

Background To our knowledge, the comparative effectiveness of commonly used conservative treatments for carpal tunnel syndrome has not been evaluated previously in primary care. We aimed to compare the clinical and cost-effectiveness of night splints with a corticosteroid injection with regards to reducing symptoms and improving hand function in patients with mild or moderate carpal tunnel syndrome. Methods We did this randomised, open-label, pragmatic trial in adults (≥18 years) with mild or moderate carpal tunnel syndrome recruited from 25 primary and community musculoskeletal clinics and services. Patients with a new episode of idiopathic mild or moderate carpal tunnel syndrome of at least 6 weeks' duration were eligible. We randomly assigned (1:1) patients (permutated blocks of two and four by site) with an online web or third party telephone service to receive either a single injection of 20 mg methylprednisolone acetate (from 40 mg/mL) or a night-resting splint to be worn for 6 weeks. Patients and clinicians could not be masked to the intervention. The primary outcome was the overall score of the Boston Carpal Tunnel Questionnaire (BCTQ) at 6 weeks. We used intention-to-treat analysis, with multiple imputation for missing data, which was concealed to treatment group allocation. The trial is registered with the European Clinical Trials Database, number 2013-001435-48, and ClinicalTrial.gov, number NCT02038452. Findings Between April 17, 2014, and Dec 31, 2016, 234 participants were randomly assigned (118 to the night splint group and 116 to the corticosteroid injection group), of whom 212 (91%) completed the BCTQ at 6 weeks. The BCTQ score was significantly better at 6 weeks in the corticosteroid injection group (mean 2·02 [SD 0·81]) than the night splint group (2·29 [0·75]; adjusted mean difference −0·32; 95% CI −0·48 to −0·16; p=0·0001). No adverse events were reported. Interpretation A single corticosteroid injection shows superior clinical effectiveness at 6 weeks compared with night-resting splints, making it the treatment of choice for rapid symptom response in mild or moderate carpal tunnel syndrome presenting in primary care