Aiming at the problems of high labor intensity and high cost of manual picking, high loss rate of mechanical picking seeds, low mechanization level and difficult to guarantee the quality of picking plates in the process of picking plates of edible sunflower. Based on the principle of manual plate taking, a plate taking control system for sunflower harvesting table was designed. Through the research and analysis of the principle of taking the plate of the edible sunflower harvesting table. According to the actual operation requirements, the overall scheme of the sunflower plate control system is determined, and the control strategy of imitating artificial low loss harvesting is designed. To reduce the grain loss in the process of taking the plate and improve the control accuracy of the system on the movement speed and displacement of the key components in the process of taking the plate, a trapezoidal acceleration and deceleration control algorithm is designed as the control algorithm of taking the plate. To verify the working performance of the plate control system, with the absolute error, relative error and total loss rate of the harvest as objectives. The bench and field verification experiments were both carried out. The bench experiment showed that the speed error of the plate parts was not more than 0.028 m/s. In the bench experiments of the device, the maximum positioning error was 1.25 mm, the average relative error is only 0.94 %, and the grain loss rate was not more than 2.26 %. It result showed that the system algorithm was reliable, the positioning accuracy was high, and the taking plate operation can be completed well. The field verification experiment showed that the forward speed of the unit was in the range of 0.4~0.8 m/s, and the total loss rate of harvest was less than 5 %. When the forward speed is 0.6 m/s, the minimum harvest loss rate is 2.32 %, and which indicated the control system meets the requirements of sunflower harvesting operation.

Many authors proposed analytical methods for solving fully fuzzy Sylvester matrix equation (FFSME) based on Vec-operator and Kronecker product. However, these methods are restricted to nonnegative fuzzy numbers and cannot be extended to FFSME with near-zero fuzzy numbers. The main intention of this paper is to develop a new numerical method for solving FFSME with near-zero trapezoidal fuzzy numbers that provides a wider scope of trapezoidal fully fuzzy Sylvester matrix equation (TrFFSME) in scientific applications. This numerical method can solve the trapezoidal fully fuzzy Sylvester matrix equation with arbitrary coefficients and find all possible finite arbitrary solutions for the system. In order to obtain all possible fuzzy solutions, the TrFFSME is transferred to a system of non-linear equations based on newly developed arithmetic fuzzy multiplication between trapezoidal fuzzy numbers. The fuzzy solutions to the TrFFSME are obtained by developing a new two-stage algorithm. To illustrate the proposed method numerical example is solved.

In this paper, improved matrix Reduction Method is proposed for the solution of fuzzy transportation problem in which all inputs are taken as fuzzy numbers. Since ranking fuzzy number is important tool in decision making, Fuzzy trapezoidal number is converting in to crisp set by using Mean techniques and solved by proposed method for fuzzy transportation problem. We give suitable numerical example for unbalanced and compare the optimal value with other techniques. The Result shows that the optimum profit of transportation problem using proposed technique under robust ranking method is better than the other method. Novelty: The numerical illustration demonstrates that the new projected method for managing the transportation problems on fuzzy algorithms.

In the paper, a modified nonlinear finite element method for analysis of trapezoidal plates geometrically reduced to shallow-shell Reissner-Mindlin formulation is presented. Due to the method proposed the complex plate cross-section and nonlinear materials may be modelled and no implementation of advanced constitutive law via user subroutines is needed. The generalized nonlinear constitutive law is used to update the stiffness of the plate element. The method enables modeling of complicated cross-sections, such as steel trapezoidal sheets, metal facing sandwich panels or reinforced concrete. Additionally, for those geometrically complex sections an advanced nonlinear material may be adopted. To verify the proposed method, a selected trapezoidal sheets were modeled in a commercial software as full 3D shell structures. By comparing displacements and forces, it was shown that both models behave almost identically, however, the simplified model has about 300-400 times less degrees of freedom, thus it is much more efficient.

To overcome the temperature effect of NaI(Tl) detectors for energy spectrometry without additional hardware, a new correction method was put forward based on pulse deconvolution, trapezoidal shaping and amplitude correction, named DTSAC. To verify this method, actual pulses from a NaI(Tl)-PMT detector were measured at different temperatures from -20℃ to 50℃. Pulse processing and spectrum synthesis showed that the position drift of the 662 keV peak was less than 3 keV, and the corresponding resolution at 662 keV of the sum spectra ranges from 6.9% to 10.60% with trapezoidal width set as 1000 ns to 100 ns. The DTSAC method corrects temperature effect by pulse processing, and need no reference peak, reference spectrum and additional circuits. The method solves the problem of correction of pulse shape and pulse amplitude at the same time, and can be used even at high counting rate.

Natural convection is intensively explored, especially in a valley-shaped trapezoidal enclosure, because of its broad presence in both technical settings and nature. This study deals with a trapezoidal cavity, which is initially filled with linearly stratified air. Though the side walls remain adiabatic, the bottom wall is heated, and the top wall is cooled. For the stratified fluid (air), the temperature of the fluid adjacent to the top and the bottom walls is the same as that of the walls. Natural convection in the trapezoidal cavity is simulated in two dimensions using numerical simulations, by varying Rayleigh numbers (Ra) from 100 to 108 with constant Prandtl number, Pr = 0.71, and aspect ratio, A = 0.5. According to numerical results, the development of transient flow within the enclosure owing to the predefined conditions for boundary may be categorized into three distinct stages: early, transitional, and steady or unsteady. The flow characteristics at each of the three phases and the impact of the Rayleigh number on the flow’s growth are stated in this study. In addition, heat transfer through the bottom and the top surfaces is described in this study.

Background: Post-operative pain and swelling are frequently observed after sinus lift procedures. The aim of the present study was a clinical evaluation of swelling and pain of two sinus lift different flaps technique measured through visual analogue scale (VAS), verbal rating scale (VRS) and infrared thermal imaging (i.e., thermography). Methods: A randomized controlled trial was conducted in fifteen patients treated for a total of 30 sinus randomly allotted into two groups. In patients of Group I, a triangular flap was performed, while in Group II modified triangular flap without anterior release was performed. Postoperative pain was scored by VAS and inflammation was recorded by VRS at 2, 4, 6 and 14 days. The facial temperature was recorded before and after sinus augmentation, at 2, 4, 6 day intervals for the first week and at 14 day, to check the course of healing. Results: In group I the pain intensity was recorded at 2 days after the surgery with a score of 38.67 ± 6.4 mm. Swelling was higher at 2 and 4 day, and it was absent at day 6. Facial temperature difference before and after the procedure was 3 (4.737 °C ± 0.37). In Group II the pain was lower than in Group I (p < 0,05). Swelling scored 2 on the first and second day, and it was reduced at day 4. After the second day the difference of temperature reduced significantly compared to day of surgery (0.77 °C), at 2 and 4 days no difference was registered. Conclusion: In conclusion based on the outcome of the present study, modified triangular flap can be used with success in sinus augmentation procedures and is to be preferred to trapezoidal flap.

Currently, a wide variety of velocity profiles are used in motion control. Thus, this paper compares the energy consumption of three parabolic, trapezoidal, and S-curve profiles. We studied the case of using embedded systems since they are a powerful solution to monitor and coordinate the movement of devices and machinery in various industries combined with motion control applications. These integrated systems allow precise and efficient control of motors and actuators through control and feedback algorithms. In addition, we propose an alternative methodology for implementing motion controllers using an Advanced RISC Machine (ARM) microcontroller, which computes the trajectory and the control action in real-time. We conducted an experiment using a linear plant composed of a direct current (DC) motor coupled to an endless screw where a carriage is mounted that can move mechanically along a rail a distance of 1.16m. In addition, a 4096 pulses per revolution (PPR) encoder is connected to the motor to measure position and angular velocity, which compute the distance the carriage has moved in meters. A current sensor is used to assess the energy consumption, and 40 tests for each profile were carried out to compare the energy consumption for the three-motion profiles considering cases with and without load on the carriage.

The relative operating characteristic (ROC) curve is a popular diagnostic tool in forecast verification, with the area under the ROC curve (AUC) used as a verification metric measuring the discrimination ability of a forecast. Along with calibration, discrimination is deemed as a fundamental probabilistic forecast attribute. In particular, in ensemble forecast verification, AUC provides a basis for the comparison of potential predictive skill of competing forecasts. While this approach is straightforward when dealing with forecasts of common events (e.g. probability of precipitation), the AUC interpretation can turn out to be oversimplistic or misleading when focusing on rare events (e.g. precipitation exceeding some warning criterion). How should we interpret AUC of ensemble forecasts when focusing on rare events? How can changes in the way probability forecasts are derived from the ensemble forecast affect AUC results? How can we detect a genuine improvement in terms of predictive skill? Based on verification experiments, a critical eye is cast on the AUC interpretation to answer these questions. As well as the traditional trapezoidal approximation and the well-known bi-normal fitting model, we discuss a new approach which embraces the concept of imprecise probabilities and relies on the subdivision of the lowest ensemble probability category.

As an important support for power system with high penetration of renewable energy, energy storage system (ESS) has changed the traditional model of simultaneous implementation of electricity production and consumption, and its installed capacity under the source-grid-load scenario is rising year by year, but it faces the problems of insufficient utilization and benefits. This study analyzes the functional combination of ESS under the source-grid-load scenarios, and proposes a comprehensive benefit evaluation method of energy storage projects based on fuzzy decision-making trial and evaluation laboratory (DEMATEL) and super efficiency data envelopment analysis (DEA) model, which considers the perspective of economic and social environment. Firstly, the functional requirements of energy storage on the source-grid-load scenarios are explored respectively, and the characteristics of various functions are analyzed to form functional combination schemes. Secondly, index modeling is carried out from three aspects: the whole life cycle cost, functional combination benefit and social environmental benefit, and the comprehensive benefit evaluation index system of energy storage project is proposed, which includes both economic and social environment. Then, the intuitionistic trapezoidal fuzzy number is combined with DEMATEL to form an effective analysis method for the input-output relationship of the indexes, and the comprehensive evaluation is realized based on the super efficiency DEA model. Finally, the effectiveness of the proposed evaluation method and the rationality of the functional combination are verified under source-grid-load scenarios respectively.

This paper proposes a novel three-phase voltage source inverter dead-time compensation strategy for accurate compensation in wide current regions of the inverter. In particular, an analysis of the output voltage distortion of the inverter, which appears as parasitic components of the switches, has been conducted for proper voltage compensation in the low current region, and an on-line compensation voltage controller has been proposed. Also, a new trapezoidal compensation voltage implementation method using the current phase is proposed to simplify realizing the trapezoidal shape of the three-phase compensation voltages. Finally, when the proposed dead-time compensation strategy is applied, the maximum phase voltage magnitude in the linear modulation voltage regions is defined to achieve smooth operation even at high modulation index. Simulations and experiments were conducted to verify the performance of the proposed dead-time compensation scheme.

In this paper we provide some bounds for the error in approximating the Riemann-Stieltjes integral $\int_{a}^{b}f (t) du (t)$ by the generalized trapezoidal rule \begin{equation*} \left[ u\left( b\right) -u\left( x\right) \right] f\left( b\right) +\left[ u\left( x\right) -u\left( a\right) \right] f\left( a\right) \end{equation*} under various assumptions for the integrand $f$ and the integrator $u$ for which the above integral exists. Applications for continuous functions of selfadjoint operators and unitary operators in Hilbert spaces are provided as well.