Accurate expression of bracket prescription is important for successful orthodontic treatment. The aim of this study was to evaluate the accuracy of digital scan images of brackets produced by four different intraoral scanners (IOSs) in terms of the height, position, and angle of the bracket slot when scanning the surface of dental model attached with bracket materials made from different composition of materials. Brackets made from stainless steel, polycrystalline alumina, composite and composite/stainless steel slot were considered, which have been scanned from 4 different IOSs (Primescan, Trios, CS3600 and i500). SEM images were used as references. Each bracket axis was set in the reference scan image, and the axis was set identically by superimposing with the IOS image, and then only the brackets were divided and analyzed. The difference between the manufacturer's nominal torque and bracket slot base angle was 0.39 in SEM, 1.96 in Primescan, 2.04 in Trios, and 5.21 in CS3600 (P <0.001). The parallelism, which is the difference between the upper and lower angles of the slot wall, was 0.55 in SEM, 7.55 in Primescan, 6.74 in Trios3, 6.59 in CS3600, and 24.95 in i500 (p <0.001). This study evaluated the accuracy of the bracket only and it must be admitted that there is some error in recognizing slots through scanning in general

During operation, the support bracket is the main part to withstand the axial loads of the pumped storage unit. Moreover, the effects of axial loads including the hydraulic thrust of runner flow and the weight of runner body may cause the support bracket deformation and fatigue damage. For the safe and stable operation, the simulation of the axial force and the structural analysis of the support bracket of a pumped storage unit was carried out in this paper. The CFD simulation result has revealed the variation rule of the axial force in different operating conditions. Using ANSYS Mechanical, the static stresses and deformation of support bracket with axial loads were calculated. The results release the location and variations of maximum stress and maximum deformation caused by the axial loads. By comparing the predicted maximum axial force with the admission force calculated by the structural analysis, it is found that the axial force of the researched machine is within the safe range. This study provides the reference for the safety and stable operation of the pumped storage unit.

We propose a generalization of Nambu-Hamilton equation in superspace $\mathbb R^{3|2}$ with three real and two Grassmann coordinates. We construct the even degree vector field in the superspace $\mathbb R^{3|2}$ by means of the right-hand sides of proposed generalization of Nambu-Hamilton equation and show that this vector field is divergenceless in superspace. Then we show that our generalization of Nambu-Hamilton equation in superspace leads to family of ternary brackets of even degree functions defined with the help of Berezinian. This family of ternary brackets is parametrized by the infinite dimensional group of invertible second order matrices, whose entries are differentiable functions on the space $\mathbb R^{3}$. We study the structure of ternary bracket in a more general case of a superspace $\mathbb R^{n|2}$ with $n$ real and two Grassmann coordinates and show that for any invertible second order functional matrix it splits into the sum of two ternary brackets, where one is usual Nambu-Poisson bracket, extended in a natural way to even degree functions in a superspace $\mathbb R^{n|2}$, and the second is a new ternary bracket, which we call $\Psi$-bracket, where $\Psi$ can be identified with invertible second order functional matrix. We prove that ternary $\Psi$-bracket as well as the whole ternary bracket (the sum of $\Psi$-bracket with usual Nambu-Poisson bracket) is totally skew-symmetric, satisfies the Leibniz rule and the Filippov-Jacobi identity (Fundamental Identity).

This paper presents laboratory devices on which experimental measurements were carried out to prove the validity of the assumption about the reduction of vibrations transmitted to the conveyor belt structure generated by the impact forces of falling material grains in the places of transfer or on the hoppers of conveyor belts. In order to limit damage to the conveyor belts caused by the impact of the sharp edges of material grains, conveyor belts are supported by impact rollers or impact rubber rods in the places of transfers and on the hoppers of belt conveyors. The flattened ends of the impact rollers are inserted into the grooves of steel brackets installed on the supports of the fixed conveyor idlers of a conventional design. In this paper, a special modification of the fixed conveyor idler is presented, which consists of inserting plastic brackets into the structurally modified roller axle holders of the fixed conveyor idler. Measurements were carried out on the first laboratory device, which showed that the specially modified fixed conveyor idler resulted in a higher damping of up to 15% of the impact forces of the falling weight on the rubberized hoop of the impact roller shell compared to the conventional fixed conveyor idler design. Measurements carried out on the second laboratory device show that the effective vibration velocity values detected at the points where the impact roller axis fits into the fixed roller table holder, i.e. points B and D, are higher than when using plastic brackets, up to 6% for a 108 mm diameter roller, compared to steel impact roller brackets.

By the study of the pattern book Ying Zao Fa Shi (building regulations of Song Dynasty, 1103 AD), while analyzing the combining and dimensioning rule of timber framework and tile work, a model self-generating program has been compiled for the first time. The operating framework has been firstly defined, while solving the issues of clustering principle, connecting method, output classification, etc. with the detailed description of algorithm theory. Taking the corner bracket set and nine-ridge roof for example, after the compilation and debug by Grasshopper, according to various input parameters, various models have been generated automatically by the plugin, proving the velocity and the veracity of the algorithm.

There is no formal difference between particles and black holes. This formal similarity lies in the intersection of gravity and quantum theory; quantum gravity. Motivated by this similarity, `wave-black hole duality' is proposed, which requires having a proper energy-momentum tensor of spacetime itself. Such a tensor is then found as a consequence of `principle of minimum gravitational potential'; a principle that corrects the Schwarzschild metric and predicts extra periods in orbits of the planets. In search of the equation that governs changes of observables of spacetime, a novel Hamiltonian dynamics of a Pseudo-Riemannian manifold based on a vector Hamiltonian is adumbrated. The new Hamiltonian dynamics is then seen to be characterized by a new `tensor bracket' which enables one to finally find the analogue of Heisenberg equation for a `tensor observable' of spacetime.