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This paper investigates the forward and inverse kinematics in screw coordinates for a planar slider-crank linkage. According to the definition of a screw, both the angular velocity of a rigid body and the linear velocity of a point on it are expressed in screw components. Through numerical integration on the velocity solution, we get the displacement. Through numerical differential interpolation of velocity, we gain the acceleration of any joint. Traditionally, position and angular parameters are usually the only variables for establishing the displacement equations of a mechanism. For a series mechanism, the forward kinematics can be expressed explicitly in the variable of position parameters while the inverse kinematics will have to resort to numerical algorithms because of the multiplicity of solution. For a parallel mechanism, the inverse kinematics can be expressed explicitly in the variable of position parameters of the end effector while the forward kinematics will have to resort to numerical algorithms because of the nonlinearity of system. Therefore this will surely lead to second order numerical differential interpolation for the calculation of accelerations. The most prominent merit of this kinematic algorithm is that we only need the first order numerical differential interpolation for computing the acceleration. To calculate the displacement, we also only need the first order numerical integral of the velocity. This benefit stems from the screw the coordinates of which are velocity components. The example of planar four-bar and five-bar slider-crank linkages validate this algorithm. It is especially suited to developing numerical algorithms for forward and inverse velocity, displacement and acceleration of a linkage.

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Teresa Crespo Vicente, [en] Group theory is quite an astonishing field of Mathematics that reminds of a big world of puzzles, starting from the very first definition of a Group to the concept of the Monster Group which is featured in many informational papers and videos. In particular, one of the most interesting approaches is the Galois theory, which was first introduced in the bachelor’s degree. We will merge this concept together with algebras to achieve the structures that this work’s title is based on, the Hopf Galois structures. These structures will be the focal point of the present thesis. The goal is to compute them using Magma (short for Magma Computational Algebra System), a software designed for computations in algebra. For that matter, we will start by presenting the preliminaries where we give concepts that might have not been shown in the bachelor’s degree. Afterwards we will give the definitions of the types of algebra to be used. It is followed by the Greither-Pareigis theory which gives the background of the Hopf Galois structures. Sought after we have the Byott’s Theorem, which has an immediate application that our program will be based on. Finally, to summarize, we will show some other results and continuations about this matter.

This paper proposes a kinematics methodology in twist coordinates for screw linkages. Based on the definition of a twist, both the angular velocity of a link and the linear velocity of a point on it may be explicitly represented in twist coordinates. Through integration on the twist solution numerically or analytically, we may obtain the displacements. By differential or numerical differential interpolation of the twist, we can find the accelerations of the link. The most outstanding advantage of this kinematic algorithm is that only the numerical differential interpolation of the first order is required to calculate the acceleration while only the first order integration of the twist is enough to compute the displacement. This merit makes it particularly fit for developing programmes to accomplish the kinematics analysis of a spatial linkage.

Understanding the key characteristics associated with genetic progress is essential to future wheat breeding strategies. Our objectives were to investigate the genetic progress in grain yield (GY) and key characteristics in wheat (Triticum aestivumL.) cultivars released from 1964 to 2007 in Hebei province, China. Field experiments including 9 milestone cultivars were conducted during three growing seasons (2010–2011, 2011–2012, and 2012–2013) at Shijiazhuang of Hebei. Grain yield is significantly increased by the linear rate of 47.4 kg ha−1 yr−1 or 0.717% (R 2 = 0.909, P

Natural and edible materials have attracted increasing attention in food packaging, which could overcome the serious environmental issues caused by conventional non-biodegradable synthetic packaging. In this work, gelatin nanofibers incorporated with two kinds of essential oil (EO), peppermint essential oil (PO) and chamomile essential oil (CO), were fabricated by electrospinning for potential edible packaging application. Electron microscopy showed that smooth and uniform morphology of the gelatin/EOs was obtained, and the diameter of nanofibers was mostly enlarged with the increase of the EO content. The proton nuclear magnetic resonance spectrum confirmed the existence of PO and CO in nanofibers after electrospinning. The addition of EOs led to an enhancement of the water contact angle of nanofibers. The antioxidant activity was significantly improved for the nanofibers loaded with CO, while the antibacteria activity against Escherichia coli and Staphylococcus aureus was better for the fibers with PO addition. The combination of half PO and half CO in nanofibers compensated for their respective limitations and exhibited optimum bioactivities. Finally, the 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide assay with NIH-3T3 fibroblasts demonstrated the absence of cytotoxicity of the gelatin/EO nanofibers. Thus, our studies suggest that the developed gelatin/PO/CO nanofiber could be a promising candidate for edible packaging.