In this paper, we show that the relative algebraic interior is a suitable replacement for both of the topological interior and the algebraic interior for the cases where these are empty. Also, we present some properties of (relative) algebraic interior and some fixed point theorems for increasing mapping. The obtained results can be viewed as an extension and improvement of the known corresponding results. Also, some examples are to support our conclusions considered.

A constrained nonlinear optimization method based on nonlinear programming techniques has been applied to map geometry of bedrock of sedimentary basins by inversion of gravity anomaly data. In the inversion, the applying model is a 2-D model that is composed of a set of juxtaposed prisms whose lower depths have been considered as unknown model parameters. The applied inversion method is a nonlinear one, which minimizes the objective functions by definition of different objective functions and an initial simple model to improve the initial model parameters.In this study, for different cases, sufficient objective functions are defined based on the condition which is encountered in the inverse problem. To control the under- determinacy part of the inverse problem and to prevent unreasonable instability in the resultant model, damping terms are added to the objective function. The act of synthetic inversion for different cases of parameterization has been examined and the results are analyzed. The results have almost depicted the recovery of the model and also fitting of the original and model response data. In addition, the method has been used to invert real gravity data in Aman Abad area. From the inversion results, depths of the basin, features like fractures and uplift in bedrock, along specific profiles have been determined. Thicker parts of sediments in the basin along the profiles have also been recognized, which have the potential for exploring drinking water in this area.

The main purpose of this paper is to obtain su cient conditions for existence of points of coincidence and common  xed points for three self mappings in b-metric spaces. Next, we obtain cone b-metric version of these results by using a scalarization function. Our results extend and generalize several well known comparable results in the existing literature.

expensive. Therefore, solutions, which can increase the quality of care and decrease costs, can be helpful. Objective: Separation of the patients based on the acute conditions can be useful in providing appropriate therapy. In this study, we present a classifier to predict the OSA based on heart rate variability of patients. Material and Methods: In this analytical study, we used the recorded ECG signals from PhysioNet Database. At first, in the preprocessing stage, the noise from the ECG signal was removed, and R spikes were detected to generate the HRV. The next stage was related to linear and non–, linear features extraction. We used the paired sample t-test that is a statistical technique to compare two periods (apnea and nonapnea). These features were applied as the inputs of two different classifiers, including MLP and SVM to find the best method and distinguish patients with higher death risk. Results: The results showed that the SVM classifier is more capable to separate the four periods seperated from each other. The sensitivity for detecting the OSA event was 95. 46% and the specificity was 97. 57% for the non-OSA period. Conclusion: Accurate and timely diagnosis of the disease can ensure the health of the individual, family, and community. Based on the proposed algorithm, the HRV signal and novel feature, presented in this study, had the highest specificity and sensitivity for the detection of the OSA event of the non-OSA, respectively.