Kumar, Surendra; Bari, Tarushree; Yadav, Subhash Kumar; Zaman, Tolga

This study presents an efficient method for estimating the population mean of a study variable using a Searls exponential ratio estimator. The approach is based on simple random sampling and leverages known population parameters of an auxiliary variable for enhanced estimation of population mean. Using large sample approximations up to the first order, the expressions for the bias and mean squared error of the proposed estimator are derived. To evaluate its performance, the estimator is compared conceptually and mathematically with several existing estimators. Theoretical results are further validated through both simulated and real-world data sets. Findings from these evaluations demonstrate that the proposed estimator consistently outperforms many competing estimators, particularly at higher population mean values. Therefore, it holds promise for improving population mean estimation across a range of practical applications.

Zaman, Tolga; Islamoglu, Ebrucan; Bulut, Hasan

This study addresses the challenge of outliers in sample surveys, a common issue that can distort results and lead to inaccurate conclusions. To tackle this problem, researchers have developed various robust regression techniques including least trimmed squares, least median of squares, least absolute deviations, Huber’s, Hample’s and Tukey’s maximum likelihood estimators, and Huber’s maximum likelihood estimator for location and scale estimators. We propose a new approach: minimum covariance determinant-based ratio estimators for estimating the population mean in sample surveys. To assess the performance of the proposed minimum covariance determinant-based estimators, we derive their mean square error expressions and determine the conditions under which they surpass existing estimators in efficiency. To validate our theoretical findings, we conduct a numerical illustration using real-world data and perform simulations with R-Programme software. The results demonstrate that our method effectively handles outliers and improves the overall accuracy of survey-based estimations, making it a valuable tool for researchers working with sample survey data.

Mazlum, Sumeyye Gur; Haliscelik, Ebru Cakil; Bektas, Ozcan

In the present study ruled surfaces generated by Darboux and instantaneous Pfaff vectors of Salkowski curves in Euclidean 3-space are considered. Some geometric properties of these surfaces such as striction curves, surface normal vectors, tangent and asymptotic planes, distribution parameters, Gaussian and mean curvatures and fundamental forms are investigated. Some results and interpretations of these surfaces are obtained.

Gungor, Nihan; Dinc, Nagihan

A novel version of the Sumudu transform is introduced by using the notion of ∗-integral, which is called non-Newtonian Sumudu transform. The fundamental characteristics of the non-Newtonian Sumudu transform are demonstrated. The obtained results are applied to the solving of non-Newtonian differential equations and growth models.

Senyurt, Suleyman; Mazlum, Sumeyye Gur; Canli, Davut; Can, Elif

In this study ruled surfaces formed by alternative unit vectors that draw these curves along Smarandache curves obtained from alternative vectors and alternative unit Darboux vectors of a differentiable curve are defined. Then the Gaussian and mean curvatures of each ruled surface are computed. It is also examined whether the surfaces are developable or minimal. Finally, examples of these surfaces are given and their graphics are drawn.

Bektas, Ozcan; Senyurt, Suleyman; Mazlum, Sumeyye Gur

The analytic properties of fuzzy sedenion numbers and sedenion valued series are studied. For this aim, we first introduce fuzzy sedenion numbers. Then we present infimum, supremum, distance, limit of sequences and other analytical properties of fuzzy sedenion numbers. We also define interval sedenion numbers and fuzzy sedenion valued series. Finally, we obtain comparison criteria of the fuzzy sedenion valued series.