Nonlocal Boundary Conditions Are Applied to the Analysis of Curve Equations

The traditional curve equation solution method has a low accuracy, so the non-local boundary conditions are applied to the curve equation solution. Firstly, the solution coordinate system is established, and then the key parameters are determined to solve the curve equation. Finally, the curve equation is solved by combining the non-local boundary conditions. The experiment proves that the method of this design is more accurate than the traditional method in solving simple curve equation or complex curve equation.

Motion of Charged Spinning Particles in a Unified Field

Using a geometry wider than Riemannian one, the parameterized absolute parallelism (PAP) geometry, we derived a new curve containing two parameters. In the context of the geometrization philosophy, this new curve can be used as a trajectory of charged spinning test particle in any unified field theory constructed in the PAP space. We show that imposing certain conditions on the two parameters, the new curve can be reduced to a geodesic curve giving the motion of a scalar test particle or/and a modified geodesic giving the motion of neutral spinning test particle in a gravitational field. The new method used for derivation, the Bazanski method, shows a new feature in the new curve equation. This feature is that the equation contains the electromagnetic potential term together with the Lorentz term. We show the importance of this feature in physical applications.

Load-Deflection Behavior of Over- and Under-Reinforced Concrete Beams with Hybrid FRP-Steel Reinforcements

The present study pertains to the load-deflection behavior and cracking moments of concrete beams with hybrid FRP-steel reinforcement. Under and over-reinforced hybrid beams were tested for failure along with reference beams with only steel or FRP reinforcement. The first-cracking moments of the beams were estimated analytically by using different uncracked moments of the inertia and modulus of rupture definitions. The uncracked moment of inertia definitions include the gross and uncracked transformed moments. The adopted modulus definitions are comprised of the experimental values from tests on prisms and the analytical values from the equations in different concrete codes. Furthermore, analytical methods were developed for estimating the deflections of concrete beams with hybrid FRP-steel or only FRP reinforcement. Two different types of elastic moduli, namely the secant modulus corresponding to the extreme compression fiber strain and the ACI 318M-19 modulus, were used in deflection calculations. Closer estimates were obtained by using the secant modulus, particularly in hybrid-reinforced beams. In the post-yielding region of the steel tension reinforcement, the deflection estimates were established to lay in closer proximity to the experimental curve when obtained by adding up the deflection increments instead of directly calculating the total deflections from the elastic curve equation. Accurate estimation of the cracking moment was found to be vital for the close prediction of deflections.

Analysis of Mechanical Behavior of Different Needle Tip Shapes During Puncture of Carbon Fiber Fabric

In the present study, the fiber-bending around the needle during the piercing process of the carbon fabric is investigated. In this regard, a mathematical model is established to investigate the bending elongation of the carbon fiber around the needle and the interaction between the carbon fiber and the needle tip. Then the mechanical behavior of the carbon fabric when moving down the tip of the steel needle is analyzed. Based on the performed analysis, a shape curve equation that satisfies the puncture needle tip is established. Furthermore, the influence of different needle tip shapes on the mechanical behavior of the carbon fiber is analyzed. The performance of the needle tip is subjected to different loads, including the puncture template, horizontal tension of the fiber to the needle tip, frictional resistance between the fiber and the needle tip, sliding force, and the bending moment. The performed analysis shows that when the shape of the needle tip assumes the form of curve 10, the downward force, horizontal tension, friction resistance, sliding force, and bending moment are minimized. Accordingly, curve 10 is proposed as the optimal shape for the needle tip. The present study is expected to provide theoretical guidance for selecting overall puncture process parameters.

Infestation and Related Ecology of Chigger Mites on the Asian House Rat (Rattus tanezumi) in Yunnan Province, Southwest China

This paper is to illustrate the infestation and related ecological characteristics of chigger mites on the Asian house rat (Rattus tanezumi). A total of 17,221 chigger mites were collected from 2,761 R. tanezumi rats, and then identified as 131 species and 19 genera in 2 families. Leptotrombidium deliense, the most powerful vector of scrub typhus in China, was the first major dominant species on R. tanezumi. All the dominant mite species were of an aggregated distribution among different individuals of R. tanezumi. The species composition and infestations of chiggers on R. tanezumi varied along different geographical regions, habitats and altitudes. The species-abundance distribution of the chigger mite community was successfully fitted and the theoretical curve equation was. Ŝ (R)=37e–(0.28R)2 The total chigger species on R. tanezumi were estimated to be 199 species or 234 species, and this further suggested that R. tanezumi has a great potential to harbor abundant species of chigger mites. The results of the species-plot relationship indicated that the chigger mite community on R. tanezumi in Yunnan was an uneven community with very high heterogeneity. Wide geographical regions with large host samples are recommended in the investigations of chigger mites.

Mathematical Description for a Particular Case of Ellipse Focus Quasi-Rotation Around an Elliptical Axis

In this paper is provided mathematical analysis related to a particular case for a point quasi-rotation around a curve of an elliptical axis. The research complements the previous works in this direction. Has been considered a special case, in which the quasi-rotation correspondence is applied to a point located at the elliptical axis’s focus. This case is special, since the quasi-rotation center search is not invariant and does not lead to determination of four quasi-rotation centers, as in the general case. A constructive approach to the rotation center search shows that any point lying on the elliptical axis can be the quasi-rotation center. This feature leads to the fact that instead of four circles, the quasi-rotation of a point lying in the elliptical axis’s focus leads to the formation of an infinite number of circle families, which together form a channel surface. The resulting surface is a Dupin cyclide, whose throat circle has a zero radius and coincides with the original generating point. While analyzing are considered all cases of the rotation center location. Geometric constructions have been performed based on previously described methods of rotation around flat geometric objects’ curvilinear axes. For the study, the mathematical relationship between the coordinates of the initial set point, the axis curve equation and the motion trajectory equation of this point around the axis curve, described in earlier papers on this topic, is used. In the proposed paper has been provided the derivation of the motion trajectory equation for a point around the elliptic axis’s curve.

Evaluation of the Japanese Fatigue Test Data in Gr.91 for Elevated Temperature Design

The ASME Boiler and Pressure Vessel Code (ASME BPVC) Section III, Division 5, Subsection HB, Subpart B provided only one design fatigue curve for Grade 91 steel (Gr.91) at 540 °C (or 1000 °F) in 2019 and earlier versions. To overcome this disadvantage, The ASME Section III Working Group on Creep-Fatigue and Negligible Creep (WG-CFNC) had taken an action to incorporate the temperature-dependent design fatigue curves for Gr. 91 developed by Japan Society of Mechanical Engineers (JSME) into ASME BPVC Section III Division 5. As a result, the temperature dependent design fatigue curves are provided in the 2021 edition of the ASME BPVC. To clear the features of the best-fit fatigue curve equation developed by the JSME, 305 data stored in the database were analyzed. Details of the database and relationship between the best-fit fatigue curve equation and the data including the statistic values and the values of 95% and 99% lower confidence bound calculated by failure probability assessment were clarified through analysis. In addition to the best-fit fatigue curve equation, an equation for dynamic stress-strain response showing the behavior of Gr.91 steel under cyclic loading of is also provided based on the same database. Moreover, some additional available data of fatigue and creep-fatigue tests obtained in Japan are also provided for considering the creep-fatigue damage evaluation under elevated temperature condition.