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This investigation deals with two new subclasses of analytic and bi-univalent functions defined by Bernoulli polynomial. In this paper, coefficient estimation and Fekete-Szego problems are solved for these newly defined function subclasses. In addition, certain remarks are indicated for the subclasses of bi-starlike and bi-convex functions. [ABSTRACT FROM AUTHOR]

Abstract–In the regression analysis, ordinary least square techniques is commonly used. However, the data's outcomes may be untrustworthy if there is an outliers in it. In order to deal with the outliers problem, robust quantile regression methods have been frequently presented as alternatives to OLS for a long time. In this article, primarily a exponential ratio-type estimators is suggested. After that, robust quantile regression estimators are proposed, that is a useful strategy. The application of robust quantile regression empowered the efficiency of the estimators especially for outliers in the data. The MSE equations of the various estimators are computed and compared to OLS approaches. Numerical illustration and simulations studies are performed to support our theoretical findings. [ABSTRACT FROM AUTHOR]

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T he researchers investigate some phenomena by continuously observing physical variables, i.e., time series. Nowadays, the Least-Squares Spectral Analysis (LSSA) technique has been preferred for the analysis of time series to conduct more reliable analysis. This technique uses the least-squares principle to estimate the hidden periodicities in the time series. Based on the previous investigations, LSSA gives more reasonable results in the experimental time series that have disturbing effects such as the datum shifts, linear trend, unequally spaced data and etc. The LSSA method is a unique method that can overcome these problems without preprocessing the original series. However, a practical and user-friendly software package in C programming language is not available for scientific purposes to implement the LSSA method. In this paper, we review the computational scheme of the LSSA method, then a software (LSSASOFT) package in the C programming language is developed in the view of the simplicity of the method and compatibility of all types of data. Finally, LSSASOFT is applied in two sample studies for the determining hidden periods in the synthetic data and sea level observations. Consequently, the numerical results indicate that LSSASOFT is a useful tool that can efficiently predicting hidden periodicity for the experimental time series that have disturbing effects. [ABSTRACT FROM AUTHOR]