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This article presents the cotangent fractional Gronwall inequality, a novel understanding of the Gronwall inequality within the context of the cotangent fractional derivative. We furnish an explanation of the cotangent fractional derivative and emphasize a selection of its distinct characteristics before delving into the primary findings. We present the cotangent fractional Gronwall inequality (Lemma 3.1) and a Corollary 3.2 using the Mittag-Leffler function, we establish singularity and compute an upper limit employing the Mittag-Leffler function for solutions in a nonlinear delayed cotangent fractional system, illustrating its practical utility. To underscore the real-world relevance of the theory, a tangible instance is given. [ABSTRACT FROM AUTHOR]

In this paper, we define and discuss the Orlicz sequence spaces ΓM(∆n u, q, s) and ΓM(p, ∆n u, q, s) of entire sequences, where (X, q) is a seminormed space and s is any real number such that s ≥ 0. Furthermore, we study some topological properties of these spaces. We discuss some inclusion relations between them and related results. [ABSTRACT FROM AUTHOR]

In this paper, straightforward and efficient brute force method is developed to slew spacecraft in the presence of static and dynamic constrained regions. Fuzzy logic is utilized to develop a fuzzy based controller that is used to control the maneuvers and test the proposed method. The controller performance is first tested in an unconstrained attitude maneuvers and then it is utilized to test the proposed method. The spacecraft is assumed to be a 3U CubeSat and the results show through Monte Carlo simulations that the controller has successfully avoided the undesired static and dynamic celestial objects. The proposed method inherits its simplicity from the geometric approach and has the ability to monitor continuously the constraints and it shows that the proposed method works in the presence of multiple constraints. [ABSTRACT FROM AUTHOR]

We present a new numerical approach to solving the fractional differential Riccati equations numerically. The approach—called the Mittag-Leffler–Galerkin method—comprises the finite Mittag-Leffler function and the Galerkin method. The error analysis of the method was studied. As a result, we present two theorems by which the error can be bounded. In addition to error analysis, the residual correction method, which allows us to estimate the error and obtain new approximate solutions, is also presented. To show how the method is applied, and the efficiency of the proposed method, some test examples were considered. When the numerical results obtained were examined, it was found that while the method achieves better results than some of the known methods in the literature, it also achieves results that are similar to those of others of the known methods. [ABSTRACT FROM AUTHOR]

Simultaneous Localization And Mapping (SLAM) is the ability of an autonomous robot to localize itself within the surroundings, while also constructing a map. It has several applications in a variety of industries, especially in indoor navigation, Autonomous driving, and robotics. This research uses an omnidirectional mobile robot to present the SLAM algorithm based on Extended Kalman Filter (EKF) in an indoor environment. Usually, SLAM combines data from odometry and other sensors, in order to overcome the accumulating error due to the wheel sliding that usually appears when using the odometry alone. Thus, in this study a Kinect sensor is used along with an odometer sensor in an unknown environment to reach a predefined point with a free collusion path using three main fuzzy controllers as part of its navigation system. The first fuzzy controller is responsible for the goal-seeking problem, where the robot moves towards the goal, the second and third controllers are responsible for static and dynamic obstacles avoidance. The robot changes its direction to avoid the static obstacles and its direction and speed to avoid the dynamic obstacles. An EV3 Lego robot is used to verify the effectiveness of the proposed study. Results shows the effectiveness of the used algorithm; the decentralized algorithm simplifies the control process, which decreases the error with the help of EKF. [ABSTRACT FROM AUTHOR]

This work presents a study in the theoretical and experimental performance of PV cells and tracking surfaces using the isotropic and anisotropic (HDKR) models' simulations for single and dual axis systems. The solar spatial and temporal coordinates are obtained for the experiment site during Julian days throughout the year. From there, further simulations are performed using Typical Meteorological Year (TMY) data to evaluate various incident irradiance parameters on tracking surfaces. Experiments with different systems including fixed, single-axis, and dual-axis systems are conducted and compared with simulation results. The simulation outcomes show a gain in PV power generation of around 6% in the anisotropic system compared to the isotropic model prototype. However, experiments show no difference between both models in dual-axis trackers. By using TMY data for optimization of tracking angles, the dual-axis trackers performance gain is 8.5% in PV power generation compared to single-axis system, and a 37% gain is observed compared to fixed-tilted PV cell. Finally, the tracking systems' optimized angles are not a function of the model used (isotropic/anisotropic) during summer months. [ABSTRACT FROM AUTHOR]

The study was conducted to examine the effect of storage temperature and duration on the viability and in vitro germination of pollen grains of seven pistachio cultivars. Pollens were stored at room temperature (24±2 oC), refrigerator (4 oC) and freezer (-5 oC) for 0, 1, 2, 3 and 4 weeks. Pollen viability was estimated by using staining methods including tetrazolium test (TTC), iodine and potassium iodine (IKI) and safranin solutions, and using an in vitro pollen germination. The results showed that at all storage methods and durations, pollen viability and in vitro pollen germination were significantly the highest for Batouri and Ashouri cultivars and the lowest for Marawhi and Elemi cultivars. The highest pollen viability as estimated by safranin staining was attained when pollens were stored under freezer condition. However, pollen viability by TTC was the lowest at room temperature storage. In addition, in vitro pollen germination and viability significantly decreased as storage duration increased. This study revealed no differences between in vitro germination percentages in refrigerated and freezer stored pollen up to 2 weeks. Meanwhile, in vitro germination of room-stored pollen gradually decreased when storage duration increased. At the end of storage period, pollen viability was reduced slightly under freezer conditions, whereas, the reduction in viability was the highest for refrigerated and room-stored pollen with no differences between them. This study showed a significant interaction effect of cultivar x storage temperature x storage duration on pollen viability but not for in vitro pollen germination. [ABSTRACT FROM AUTHOR]

Last decade witnessed a significant research effort directed towards heat sink design to improve its performance. Conventional heat sinks consist of parallel plates or pin fins. Ladder heat sink design is one of the effective recent designs formed by inserting a link between two parallel plates. In this work, the performance of ladder heat sink design is studied and compared with two designs, namely; elliptical and parallel plate heat sink designs. A computational simulation of the heat sink designs carried away using COMSOL Multiphysics software. Adaptive Neuro Fuzzy Inference System (ANFIS) is used to predict the pressure drop value with changing the dimensions of the heat sink fins, namely; length, width and height, and comparing the results with COMSOL values. Results show that ladder heat sink design has better performance in comparison with the other heat sink designs according to many parameters used to characterize the performance of the heat sink design, namely; pressure drop, temperature, cooling power and fluid velocity. Also, ANFIS shows accurate results in predicting the pressure drop value compared with the accurate value obtained from COMSOL Multiphysics. [ABSTRACT FROM AUTHOR]

In this paper, we propose an approximate solution method, called multistage Bernstein collocation method (MBCM), to solve strongly nonlinear damped systems. The method is given with an error analysis. The systems investigated include step function external excitation and periodical function external excitation. We found that the MBCM gives more accurate approximate solutions than the standard collocation method. Since MBCM splits the domain of the problem [a,b] into n parts, one can overcome oscillations arising from the standard collocation method by increasing n. The results obtained from MBCM compare favorably with that of the fourth-order Runge–Kutta method (RK4). [ABSTRACT FROM AUTHOR]