A SOLITARY CONVERGENT PERIODIC SOLUTION OF THE INVERSE TRULY NONLINEAR OSCILLATOR BY MODIFIED MICKENS’ EXTENDED ITERATION PROCEDURE

The inverse truly nonlinear oscillator is the most applied in the field of computer science, information technology, physics, electrical engineering, and mechanical engineering. The solution of the inverse truly nonlinear oscillator has been obtained by modified Mickens’ extended iteration procedure. To determine the solution of the oscillator a special type of Fourier series has been used. The iterated solutions are convergent as the second, third, and fourth approximate frequencies of the oscillator show a good concurrence with the exact result. Some researchers presented the solutions of the same oscillator by applying different methods. We have compared the obtained results with some previously published results. Some of their techniques diverge at higher-order stages but the present technique is convergent there. The method is mainly illustrated in the strongly nonlinear inverse oscillator, but it can be widely applicable in other problems arising from nonlinear sciences and engineering.

Iterative Parameter Optimization for Multiple Switching Control Applied to a Precision Stage for Microfabrication

This paper proposes an iteration procedure to derive optimal parameters for a multiple switching control architecture. Control design is usually a compromise between various performance requirements; therefore, switching between multiple controllers that achieve a particular performance under different conditions can potentially improve the overall system behavior. In this paper, we consider a control-switching mechanism that can automatically switch controllers based on the prediction of future responses, and we develop an iteration procedure that can optimize the mechanism parameters, such as the number of controllers and the prediction horizon. We then implement the proposed mechanism in a long-stroke precision stage, and demonstrate the effectiveness of switching robust control with simulations and experiments. Lastly, we integrate the stage with a two-photon polymerization system to fabricate microlenses. The optical properties confirm that the proposed iterative parameter optimization procedure is effective in improving the performance of microfabrication employing multiple switching control.

Common Fixed Points of Two G -Nonexpansive Mappings via a Faster Iteration Procedure

In this work, we study the convergence of a new faster iteration in which two G -nonexpansive mappings are involved in the setting of uniformly convex Banach spaces with a directed graph. Moreover, by constructing a numerical example, we show the fastness of our iteration procedure over other existing iteration procedures in the literature.

RD-systems with chemotaxis: global existence, boundedness and blow-up of solutions

result shows that the blow-up is equivalent to the blow-up of the $L^r-$norms of the solutions for $r$ exceeding some critical value $r_c.$ Under very loose conditions we give the estimation of $r_c,$ relying on a variant of Gagliardo-Nirenberg inequality, and a kind of bootstrap method which is very similar to the Alikakos-Moser iteration procedure.

On Iteration Sn for Operators with Condition (D)

A recently introduced nonexpansive-type condition is subjected to an in-depth analysis. New examples are provided to highlight the relationship with Suzuki-type mappings. Furthermore, a convergence survey is conducted based on the iteration procedure Sn. Issues related to data dependence and the stability of this iterative process are also being studied. Our study is performed in the framework of Banach spaces, in which the symmetry of the associated metric is a fundamental axiom and plays a key role while proving many results of this paper.

Soil Moisture Estimation for the Chinese Loess Plateau Using MODIS-derived ATI and TVDI

Timely and effective estimation and monitoring of soil moisture (SM) provides not only an understanding of regional SM status for agricultural management or potential drought but also a basis for characterizing water and energy exchange. The apparent thermal inertia (ATI) and Temperature Vegetation Dryness Index (TVDI) are two widely used indices to reflect SM from remote sensing data. While the ATI-based model is routinely used to estimate the SM of bare soil and sparsely vegetated areas, the TVDI-based model is more suitable for areas with dense vegetation coverage. In this study, we present an iteration procedure that allows us to identify optimal Normalized Difference Vegetation Index (NDVI) thresholds for subregions and estimate their relative soil moisture (RSM) using three models (the ATI-based model, the TVDI-based model, and the ATI/TVDI joint model) from 1 January to 31 December 2017, in the Chinese Loess Plateau. The initial NDVI (NDVI0) was first introduced to obtain TVDI value and two other thresholds of NDVIATI and NDVITVDI were designed for dividing the whole area into three subregions (the ATI subregion, the TVDI subregion, and the ATI/TVDI subregion). The NDVI values corresponding to maximum R-values (correlation coefficient) between estimated RSM and in situ RSM measurements were chosen as optimal NDVI thresholds after performing as high as 48,620 iterations with 10 rounds of 10-fold cross-calibration and validation for each period. An RSM map of the whole study area was produced by merging the RSM of each of the three subregions. The spatiotemporal and comparative analysis further indicated that the ATI/TVDI joint model has higher applicability (accounting for 36/38 periods) and accuracy than the ATI-based and TVDI-based models. The highest average R-value between the estimated RSM and in situ RSM measurements was 0.73 ± 0.011 (RMSE—root mean square error, 3.43 ± 0.071% and MAE—mean absolute error, 0.05 ± 0.025) on the 137th day of 2017 (DOY—day of the year, 137). Although there is potential for improved mapping of RSM for the entire Chinese Loess Plateau, the iteration procedure of identifying optimal thresholds determination offers a promising method for achieving finer-resolution and robust RSM estimation in large heterogeneous areas.

Failure rate properties of parallel systems

We study failure rate monotonicity and generalised convex transform stochastic ordering properties of random variables, with an emphasis on applications. We are especially interested in the effect of a tail-weight iteration procedure to define distributions, which is equivalent to the characterisation of moments of the residual lifetime at a given instant. For the monotonicity properties, we are mainly concerned with hereditary properties with respect to the iteration procedure providing counterexamples showing either that the hereditary property does not hold or that inverse implications are not true. For the stochastic ordering, we introduce a new criterion, based on the analysis of the sign variation of a suitable function. This criterion is then applied to prove ageing properties of parallel systems formed with components that have exponentially distributed lifetimes.