Optimal Convergence Rate for Mirror Descent Methods with special Time-Varying Step Sizes Rules

In this paper, the optimal convergence rate $O\left(N^{-1/2}\right)$ (where $N$ is the total number of iterations performed by the algorithm), without the presence of a logarithmic factor, is proved for mirror descent algorithms with special time-varying step sizes, for solving classical constrained non-smooth problems, problems with the composite model and problems with non-smooth functional (inequality types) constraints. The proven result is an improvement on the well-known rate $O\left(\log (N) N^{-1/2}\right)$ for the mirror descent algorithms with the time-varying step sizes under consideration. It was studied a new weighting scheme assigns smaller weights to the initial points and larger weights to the most recent points. This scheme improves the convergence rate of the considered mirror descent methods, which in the conducted numerical experiments outperform the other methods providing a better solution in all the considered test problems.Comment: Preprint under updat

التوافق المهني لدى عينة من الموظفين في المديرية العامة للتربية والتعليم بمحافظة الداخلية بسلطنة عمان

The current research investigates the Occupational Adjustment of a sample of employees at the Directorate General of Education in AlDakhliyah governorate. The researchers have used a descriptive correlational approach and the research was conducted with 260 employees working in the directorate general of the governorate. A research instrument was designed by the researchers to measure the occupational adjustment. The main results indicated that the level of occupational adjustment of the research sample appears to be very high. There were no statistically significant differences in the level of occupational adjustment due to social status and qualification. However, there were statistically significant differences in the level of occupational adjustment due to gender in favor for the male employees. Also, it was found that there were statistically significant differences in the level of occupational adjustment due to years of experience in favor for those with more than 15 years of experienc

Electrothermally Actuated Microbeams With Varying Stiffness

We present axially loaded clamped-guided microbeams that can be used as resonators and actuators of variable stiffness, actuation, and anchor conditions. The applied axial load is implemented by U-shaped electrothermal actuators stacked at one of the beams edges. These can be configured and wired in various ways, which serve as mechanical stiffness elements that control the operating resonance frequency of the structures and their static displacement. The experimental results have shown considerable increase in the resonance frequency and mid-point deflection of the microbeam upon changing the end conditions of the beam. These results can be promising for applications requiring large deflection and high frequency tunability, such as filters, memory devices, and switches. The experimental results are compared to multi-physics finite-element simulations showing good agreement among them.</jats:p

A Highly Sensitive and Wide-Range Resonant Magnetic Micro-Sensor Based on A Buckled Micro-Beam

Abstract We experimentally demonstrate a miniature highly sensitive wide-range resonant magnetic Lorentz-force micro-sensor. The concept is demonstrated based on the detection of the resonance frequency of an in-plane electrothermally heated straight resonator operated near the buckling point. The frequency shift is measured with optical sensing and the device is operating at atmospheric pressure. The magnetometer demonstrates a sensitivity (S) of 33.9/T, which is very high compared to the state of the art. In addition, the micro-sensor shows a good linearity in wide range and low power consumption around 0.2 mW. The above performances make the proposed micro-sensor promising for various low-cost magnetic applications.</jats:p

Tunable Clamped–Guided Arch Resonators Using Electrostatically Induced Axial Loads

We present a simulation and experimental investigation of bi-directional tunable in-plane clamped-guided arch microbeam resonators. Tensile and compressive axial forces are generated from a bi-directional electrostatic actuator, which modulates the microbeam stiffness, and hence changes its natural frequency to lower or higher values from its as-fabricated value. Several devices of various anchor designs and geometries are fabricated. We found that for the fabricated shallow arches, the effect of the curvature of the arch is less important compared to the induced axial stress from the axial load. We have shown that the first mode resonance frequency can be increased up to twice its initial value. Additionally, the third mode resonance frequency can be increased up to 30% of its initial value. These results can be promising as a proof-of-concept for the realization of wide-range tunable microresonators. The experimental results have been compared to finite-element simulations, showing good agreement among them

Static and Dynamic Analysis of Electrostatically Actuated MEMS Shallow Arches for Various Air-Gap Configurations

In this research, we investigate the structural behavior, including the snap-through and pull-in instabilities, of in-plane microelectromechanical COSINE-shaped and electrically actuated clamped-clamped micro-beams resonators. The work examines various electrostatic actuation patterns including uniform and non-uniform parallel-plates airgap arrangements, which offer options to actuate the arches in the opposite and same direction of their curvature. The nonlinear equation of motion of a shallow arch is discretized into a reduced-order model based on the Galerkin’s expansion method, which is then numerically solved. Static responses are examined for various DC electrostatic loads starting from small values to large values near pull-in and snap-through instability ranges, if any. The eigenvalue problem of the micro-beam is solved revealing the variations of the first four natural frequencies as varying the DC load. Various simulations are carried out for several case studies of shallow arches of various geometrical parameters and airgap arrangements, which demonstrate rich and diverse static and dynamic behaviors. Results show few cases with multi-states and hysteresis behaviors where some with only the pull-in instability and others with both snap-through buckling and pull-in instabilities. It is found that the micro-arches behaviors are very sensitive to the electrode’s configuration. The studied configurations reveal different possibilities to control the pull-in and snap-through instabilities, which can be used for improving arches static stroke range as actuators and for realizing wide-range tunable micro-resonators

Effect of Initial Curvature on the Static and Dynamic Behavior of MEMS Resonators

In this paper, we investigate experimentally and analytically the effect of the initial shape, arc and cosine wave, on the static and dynamic behavior of microelectromechanical (MEMS) resonators. We show that by carefully choosing the geometrical parameters and the shape of curvature, the veering phenomenon (avoided-crossing) between the first two symmetric modes can be activated. To demonstrate this concept, we study electrothermally tuned and electrostatically driven MEMS initially curved resonators. Applying electrothermal voltage heats up the beams and then increases their curvature (stiffness) and controls their resonance frequencies. While changing the electrothermal voltage, we demonstrate high frequency tunability of arc resonators compared to the cosine-configuration resonators for the first and third resonance frequencies. For arc beams, we show that the first resonance frequency increases up to twice its fundamental value and the third resonance frequency decreases until getting very close to the first resonance frequency triggering the veering phenomenon. Around the veering regime, we study experimentally and analytically, using a reduced order model based on a nonlinear Euler-Bernoulli shallow arch beam model, the dynamic behavior of the arc beam for different electrostatic forcing.</jats:p