On Curvatures of the Torus Hypersurface in 4-Space

We study curvatures of torus hypersurface in the four dimensional Euclidean space. We also give some relations on  of torus hypersurface

Generalized Helical Hypersurfaces Having Time-like Axis in Minkowski Spacetime

In this paper, the generalized helical hypersurfaces x=x(u,v,w) with a time-like axis in Minkowski spacetime E14 are considered. The first and the second fundamental form matrices, the Gauss map, and the shape operator matrix of x are calculated. Moreover, the curvatures of the generalized helical hypersurface x are obtained by using the Cayley–Hamilton theorem. The umbilical conditions for the curvatures of x are given. Finally, the Laplace–Beltrami operator of the generalized helical hypersurface with a time-like axis is presented in E14

RIGHT CONOID HYPERSURFACES IN FOUR-SPACE

The right conoid hypersurfaces in the four-dimensional Euclidean space $\mathbb{E}^{4}$ are introduced. The matrices corresponding to the fundamental form, Gauss map, and shape operator of these hypersurfaces are calculated. By utilizing the Cayley--Hamilton theorem, the curvatures of these specific hypersurfaces are determined. Furthermore, the conditions for minimality are presented. Additionally, the Laplace--Beltrami operator of this family is computed, and some examples are provided

THE EVALUATION OF MENTAL ABILITIES OF ATHLETES IN DIFFERENT BRANCHES

This paper aims to evaluate the levels of mental ability of licensed athletes who are actively engaged in sports at branch level in Turkey. A total of 340 athletes, including 116 women and 224 men, from various regions of Turkey who are actively engaged in sports at elite level in different branches voluntarily participated in the survey which evaluates their levels and techniques of mental training. It was considered important that athletes participated in the survey should be licensed and importance of the study was emphasized to them. The survey model was used in this study. Current information related to research problem was systematically given by scanning of relevant literature, so a theoretical framework on the subject was created. First of all, a twelve-question personal information form developed by researcher was applied. Ottawa Mental Skills Assessment tool (OMSAT-3) which is developed by Durand-Bush, Salmela and Green-Demers (2001) and adapted to Turkish language by Erhan, Güler, Ağduman and Gerek was applied to evaluate the levels of athletes’ mental ability. In the adaptation phase, the scale was applied to 220 athletes and internal consistency value was found to be 0.94. The scale consists of 48 items and 12 subscales and these subscales are evenly divided into four items. The scale consists of a total of 48 items and constructed on a 7-point Likert-type. The scoring was formed from 1 to 7 according to the statements, “Strongly disagree”, “Disagree”, “Slightly disagree”, “Neither agree nor disagree”, “Agree”, “Slightly agree” and “Strongly agree”. Frequency Analysis was applied to determine the demographic characteristics of participants and Shapiro-Wilk Test was applied in order to decide whether the questionnaires are suitable to normal distribution and Mann-Whitney U test was applied in order to determine the dimensions according to parameters such as gender, marital status, and type of sports, level of contact and level of sport. Kruskal-Wallis H test was applied for analysis of the dimensions in terms of age, sports age and educational level. Finally, correlation analysis of Spearman was used in order to determine the relation between sub-dimensions of total satisfaction score. The significance level (p<0.05) was accepted in analysis. As a result, there is a significant difference in mental ability dimensions of active athletes in different branches according to their mental ability levels and variables such as age, type of sports, sports level and sports age. Therefore, it is observed that mental ability levels of athletes in different branches vary according to these variables.Article visualizations

BI-ROTATIONAL HYPERSURFACE WITH Δx=Ax IN 4-SPACE

We introduce the bi-rotational hypersurface $\mathbf{x(}u,v,w\mathbf{)}$ in the four dimensional Euclidean geometry ${\mathbb{E}}^{4}.$ We obtain the $i$-th curvatures of the hypersurface. Moreover, we consider the Laplace--Beltrami operator of the bi-rotational hypersurface satisfying $\Delta \mathbf{x=}\mathcal{A}\mathbf{x}$ for some $4\times 4$ matrix $\mathcal{A}$

New Sequence Spaces with Respect to a Sequence of Modulus Functions

In this paper, we introduce the notions of  -invariant convergence, -invariant convergence with respect to a sequence of modulus functions and establish some basic theorems. Furthermore, we give some properties of   -Cauchy sequence and   -Cauchy sequence. We basically study some connections between -invariant statistical convergence and  -invariant lacunary statistical convergence with respect to a sequence of modulus functions and between strongly  -invariant convergence and  -invariant lacunary statistical convergence with respect to a sequence of modulus functions. Also, we establish some inclusion relations between new concepts of  statistically convergence and  –invariant statistically convergence with respect to a sequence of modulus functions