Existence and boundary behavior of weak solutions for Schrödingerean TOPSIS equations

Abstract In this paper, we prove that there exists a weak solution for Schrödingerean technique for order performance by similarity (TOPSIS) equations on cylinders. Meanwhile, the boundary behaviors of it are also obtained via the abstract theory of fuzzy multi-criterion decision making. As the main tools, we use Karamata regular variation theory and the method of upper and lower solutions

Effects of Asymmetries on the Dynamics of Motorized Momentum Exchange Tether and Payloads Injection Precision

This paper presents the error dynamic model of motorized momentum exchange tether (MMET) based on the momentum exchange principle of space tether. The error dynamics are caused by the structural bias of the differences in tethers’ length and the difference in payloads’ mass. After that, the coupling analysis between orbit and attitude is presented. It is shown that, with increasing the differences in tethers’ length and payloads’ mass, the COM deviation of the MMET increases linearly. The numerical simulations of the MMET by considering the structural asymmetries are presented; the results show that the asymmetries have tiny influences on the orbit of the chief satellite by decreasing the apogee, which will change the instantaneous velocity at the apogee and affect the payload injection precision. What is more, the structural asymmetries have effects on the attitude elements (including the pitch angle and yaw angle); however, the effects could be weakened by the external torque. The structural asymmetries and gravity gradient torque have composite effects on the angular velocity of the propulsion tether

Active Manipulation of the Spin and Orbital Angular Momentums in a Terahertz Graphene-Based Hybrid Plasmonic Waveguide

Angular momentums (AMs) of photons are crucial physical properties exploited in many fields such as optical communication, optical imaging, and quantum information processing. However, the active manipulation (generation, switching, and conversion) of AMs of light on a photonic chip remains a challenge. Here, we propose and numerically demonstrate a reconfigurable graphene-based hybrid plasmonic waveguide (GHPW) with multiple functions for on-chip AMs manipulation. Its physical mechanism lies in creating a switchable phase delay of ±π/2 between the two orthogonal and decomposed linear-polarized waveguide modes and the spin-orbit coupling in the GHPW. For the linear-polarized input light with a fixed polarization angle of 45°, we can simultaneously switch the chirality (with −ħ/+ħ) of the transverse component and the spirality (topological charge ℓ = −1/+1) of the longitudinal component of the output terahertz (THz) light. With a switchable phase delay of ±π in the GHPW, we also developed the function of simultaneous conversion of the charity and spirality for the circular-polarized input light. In addition, a selective linear polarization filtering with a high extinction ratio can be realized. With the above multiple functions, our proposed GHPWs are a promising platform in AMs generation, switching, conversion, and polarization filtering, which will greatly expand its applications in the THz photonic integrated circuits

Cement-Modified Loess Base for Intercity Railways: Mechanical Strength and Influencing Factors Based on the Vertical Vibration Compaction Method

Cement-modified loess has been used in the recent construction of an intercity high-speed railway in Xi’an, China. This paper studies the mechanical strength of cement-modified loess (CML) compacted by the vertical vibration compaction method (VVCM). First, the reliability of VVCM in compacting CML is evaluated, and then the effects of cement content, compaction coefficient, and curing time on the mechanical strength of CML are analyzed, establishing a strength prediction model. The results show that the correlation of mechanical strength between the CML specimens prepared by VVCM in the laboratory and the core specimens collected on site is as high as 83.8%. The mechanical strength of CML initially show linear growth with increasing cement content and compaction coefficient. The initial growth in CML mechanical strength is followed by a later period, with mechanical strength growth slowing after 28 days. The mechanical strength growth properties of the CML can be accurately predicted via established strength growth equations. The results of this study can guide the design and construction of CML subgrade

Influence of Vanadium on the Microstructure and Mechanical Properties of Medium-Carbon Steels for Wheels

Steels used for high-speed train wheels require a combination of high strength, toughness, and wear resistance. In 0.54% C-0.9% Si wheel steel, the addition of 0.075 or 0.12 wt % V can refine grains and increase the ferrite content and toughness, although the influence on the microstructure and toughness is complex and poorly understood. We investigated the effect of 0.03, 0.12, and 0.23 wt % V on the microstructure and mechanical properties of medium-carbon steels (0.54% C-0.9% Si) for train wheels. As the V content increased, the precipitation strengthening increased, whereas the grain refinement initially increased, and then it remained unchanged. The increase in strength and hardness was mainly due to V(C,N) precipitation strengthening. Increasing the V content to 0.12 wt % refined the austenite grain size and pearlite block size, and increased the density of high-angle ferrite boundaries and ferrite volume fraction. The grain refinement improved the impact toughness. However, the impact toughness then reduced as the V content was increased to 0.23 wt %, because grain refinement did not further increase, whereas precipitation strengthening and ferrite hardening occurred

Evolution of microstructure and mechanical properties of cold-drawn small-caliber 16MnNiV seamless steel tube

16MnNiV steel is developed from 16Mn and 16MnV steel. After hot-perforated rolling into tube, cold rolling, cold drawing and heat treatment are carried out to prepare high pressure tubes with high caliber. The microstructure and mechanical properties of 16MnNiV seamless steel tube of small diameter were studied by means of optical microscopy (OM), scanning electron microscopy (SEM), electron backscattering diffraction (EBSD), transmission electron microscopy (TEM) and physicochemical phase analysis. The microstructure and the change of the second phase precipitation were revealed, and the strengthening increment was calculated. The relevant results can provide a reference for the material development and performance improvement of high strength high pressure tubes. The results show that the main structure of the experimental steel in the process of drawing the tube is ferrite and pearlite. In the case of precipitation, annealing after one pull increases the total amount of precipitation, and annealing after the second pull does not change the total amount of precipitation. It is known from EDS analysis that the precipitated second phase particle is VC. The tensile strength and yield strength of the experimental steel are gradually increased and the elongation rate decreases after cold drawing and different heat treatment processes. It can be seen that the increase of yield strength of experimental steel mainly comes from the contribution of fine crystal reinforcement due to the large deformation of cold extraction process. After heat treatment, the tensile strength, yield strength and elongation rate of ϕ6.35 mm×3 mm round tubes reach over 960, 864 MPa and 15.5%. Compared with other high pressure tubing products of 16Mn series, the mechanical properties are greatly improved and good strong plastic matching is obtained

New applications of Schrödinger type inequalities in the Schrödingerean Hardy space

Abstract As new applications of Schrödinger type inequalities obtained by Jiang (J. Inequal. Appl. 2016: Article ID 247, 2016) in the Schrödingerean Hardy space, we not only obtain the representation of Schrödingerean harmonic functions but also give a sufficient and necessary condition between the Schrödingerean distributional function and its derivative in the Schrödingerean Hardy space