Kazan, Ahmet; Kazan, Sema; Gur Mazlum, Sumeyye; Karaca, Emel; Altin, Mustafa; Grilli, Luca

In this paper, we deal with the canal hypersurfaces that are formed as the envelope of a family of pseudo-hyperspheres or pseudo-hyperbolic hyperspheres with centers lying on a pseudo-null curve with Bishop vector fields in four-dimensional Lorentz-Minkowski space. We give main theorems which contain the parametric expressions of these canal hypersurfaces along with their Gaussian, mean, and principal curvatures and important geometric characterizations. We also provide these characterizations for tubular hypersurfaces. Finally, we construct an example to allow for better understanding and comprehension of the results.

Ali, Mustafa Ahmed; Merdan, Mehmet

This study presents the Yang Transform Adomian Decomposition Method (YTADM), a semi-analytical framework for solving one-dimensional linear and nonlinear delay fractional partial differential equations involving the Caputo fractional derivative. The proposed method combines the Yang transform with the Adomian decomposition method to construct recursive solution series while efficiently handling delayed nonlinear terms. The applicability of the proposed framework is demonstrated through several examples, including proportional-delay Burgers-type equations, and its convergence properties are analyzed. The obtained results show that YTADM yields rapidly convergent semi-analytical approximations and provides an effective framework for solving one-dimensional delay fractional partial differential equations.

Cona, Lale; Şimşek, Deniz

This article addresses the convergence of iteration sequences in Cesàro means for asymptotically nonexpansive mappings. Specifically, this study explores the behavior of Kirk iteration in the Cesàro means in the context of uniformly convex and reflexive Banach spaces equipped with uniformly Gâteaux differentiable norms. The focus is to determine the conditions under which the Kirk iteration sequence converges strongly or weakly to a fixed point. Finally, some examples are given in this article to demonstrate the advantages of the preferred iteration method and to verify the results obtained.

Şahin, Yasin; Merdan, Mehmet; Açıkgöz, Pınar

This paper proposes a novel analytical method to address the Helmholtz fractional differential equation by combining the Aboodh transform with the Adomian Decomposition Method, resulting in the Aboodh–Adomian Decomposition Method (A-ADM). Fractional differential equations offer a comprehensive framework for describing intricate physical processes, including memory effects and anomalous diffusion. This work employs the Caputo–Fabrizio fractional derivative, defined by a non-singular exponential kernel, to more precisely capture these non-local effects. The classical Helmholtz equation, pivotal in acoustics, electromagnetics, and quantum physics, is extended to the fractional domain. Following the exposition of fundamental concepts and characteristics of fractional calculus and the Aboodh transform, the suggested A-ADM is employed to derive the analytical solution of the fractional Helmholtz equation. The method’s validity and efficiency are evidenced by comparisons of analytical and approximation solutions. The findings validate that A-ADM is a proficient and methodical approach for addressing fractional differential equations that incorporate Caputo–Fabrizio derivatives.

Gür Mazlum, Sümeyye; Şenyurt, Süleyman; Grilli, Luca

In this paper, we calculate the Gaussian curvatures of the dual spherical indicatrix curves formed on unit dual sphere by the Blaschke vectors and dual instantaneous Pfaff vectors of dual parallel equidistant ruled surfaces (DPERS) and we give the relationships between these curvatures. In addition to—in cases where the base curves of these DPERS are closed—computing the dual integral invariants of the indicatrix curves. Additionally, we show the relationships between them. Finally, we provide an example for each of these indicatrix curves.

Gür Mazlum, Sümeyye; Şenyurt, Süleyman; Grilli, Luca

In this study, we examine the dual expression of Valeontis’ concept of parallel p-equidistant ruled surfaces well known in Euclidean 3-space, according to the Study mapping. Furthermore, we show that the dual part of the dual angle on the unit dual sphere corresponds to the p-distance. We call these ruled surfaces we obtained “dual parallel equidistant ruled surfaces” and we briefly denote them with “DPERS”. Furthermore, we find the Blaschke vectors, the Blaschke invariants and the striction curves of these DPERS and we give the relationships between these elements. Moreover, we show the relationships between the Darboux screws, the instantaneous screw axes, the instantaneous dual Pfaff vectors and dual Steiner rotation vectors of these surfaces. Finally, we give an example, which we reinforce this article, and we explain all of these features with the figures on the example. Furthermore, we see that the corresponding dual curves on the dual unit sphere to these DPERS are such that one of them is symmetric with respect to the imaginary symmetry axis of the other.

Yalcin, Fusun; Ilbeyli, Nurdane; Demirbilek, Mehmet; Yalcin, Mustafa Gurhan; Gunes, Alper; Kaygusuz, Abdullah; Ozmen, Suleyman Fatih

The study aimed to determine the natural radioactivity levels of226Ra,232Th, and40K by the Gamma-Ray spectrometry method, and radiological hazard parameters of the plutonic rocks in the Western and Central Sakarya Zone and to analyze the data using multivariate statistical methods. The average radiological values of samples were determined as40K (1295.3 Bq kg−1) >232Th (132.1 Bq kg−1) >226Ra (119.7 Bq kg−1). According to the skewness values of the distributions of the examined radionuclides,226Ra (2.1) and232Th (0.7) seemed to be positively right-skewed while40K (−0.2) had a negatively right-skewed histogram. On the other hand, the following kurtosis values were calculated for the distributions:226Ra (5.8 > 3),232Th (−0.7), and40K (−0.8). Kolmogorov–Smirnov and Shapiro–Wilk tests were applied to the data to test their normality. Therefore, Spearman’s correlation coefficient method was performed. The radionuclides of226Ra and232Th were found to have a positive correlation with radiological hazard parameters of the samples. 2 (two)-related factors identified, and the cumulative value was calculated to be 98.7% on the basis of the Scree Plot. According to the hierarchical cluster analysis, the samples that are grouped with those from Camlik region are prominent. The average radioactivity values of Camlik, Sogukpinar, Karacabey, and Sogut (except for232Th) regions were detected to be higher than the world averages while the value of40K was also found to be higher than the average values of various countries in the world.