Aktaş, İbrahim

Accurate precursor calculation is essential for the successful synthesis of oxide-based superconductors. This study compares two commonly used methods stoichiometric balance and conversion factor (CF) approaches in the synthesis of YBa2Cu3O7-δ (Y123) and Y3Ba5Cu8O18+δ (Y358) superconductors. The analysis reveals that CF methods introduce substantial systematic errors, particularly for Y2O3, with deviations reaching 21.2% in Y123. These errors are exacerbated in Y358 due to its increased stoichiometric complexity. Unlike stoichiometric methods, CF approaches neglect volatile losses such as CO2 and fail to adjust for oxygen non-stoichiometry (δ variations), leading to misestimations in precursor masses. Statistical tests (χ2 < 0.001, RMSE) and experimental data confirm that these inaccuracies can negatively impact phase purity and crystallographic quality. A strong correlation (R2 = 0.847) between stoichiometric accuracy and phase formation quality emphasizes the importance of rigorous calculation. This study highlights the inherent limitations of CF-based shortcuts and underscores the necessity of comprehensive stoichiometric modeling, especially in complex oxide systems. The findings also provide an educational framework to address common misconceptions in materials synthesis, particularly for early-stage researchers in solid-state chemistry and materials science.

Aktaş, İbrahim; Baricz, Árpád; Singh, Sanjeev

Some geometric properties of a normalized hyper-Bessel functions are investigated. Especially we focus on the radii of starlikeness, convexity, and uniform convexity of hyper-Bessel functions and we show that the obtained radii satisfy some transcendental equations. In addition, we give some bounds for the first positive zero of normalized hyper-Bessel functions, Redheffer-type inequalities, and bounds for this function. In this study we take advantage of Euler–Rayleigh inequalities and Laguerre–Pólya class of real entire functions, intensively.

Aktaş, İbrahim

Bu makalenin temel amacı normalize edilmiş hata fonksiyonunun kısmi toplamlarına oranının reel kısımları için bazı alt sınırlar belirlemektir. Ek olarak, normalize edilmiş hata fonksiyonu ve türevinin mutlak değerleri için bazı üst sınırlar da verilmiştir.

Toklu, Evriim; Aktas, Ibrahim; Sagsöz, Fatma

The aim of this investigation is to introduce two new subclasses of the class sigma related with the generalized Salagean differential operator and find estimates on the coefficients vertical bar a(2)vertical bar and vertical bar a(3)vertical bar for functions in these new subclasses. Moreover, we give some interesting results by using the relationship between Salagean's differential operator and generalized Salagean differential operator.

Aktaş, I.

In this study, by using the Hadamard product representation of the hyper- Bessel function and basic concepts in mathematics we investigate the sign of the hyper- Bessel function x → J αd (x) on some sets. Also, we show that the function x → J αd (x) is a decreasing function on [0, J αd ,1), and the function is an increasing function on (0,∞), where j αd ,1 and II αd denote the first positive zero of the function J αd (x) and modified hyper-Bessel function, respectively. In addition, we prove the strictly log-concavity of the functions J αd (x) and J αd (x) on some sets. Moreover, we give some illustrative examples regarding our main results.

Aktaş, Ibrahim; Toklu, Evrim; Orhan, Halit

In this investigation our main aim is to determine the radii of uniform convexity of selected normalized q -Bessel and Wright functions. Here we consider six different normalized forms of q -Bessel functions and we apply three different kinds of the normalization of the Wright function. We also show that the obtained radii are the smallest positive roots of some functional equations.

Aktaş, Ibrahim; Baricz, Árpád; Orhan, Halit

In this paper we consider some normalized Bessel, Struve, and Lommel functions of the first kind and, by using the Euler-Rayleigh inequalities for the first positive zeros of a combination of special functions, we obtain tight lower and upper bounds for the radii of starlikeness of these functions. By considering two different normalizations of Bessel and Struve functions we give some inequalities for the radii of convexity of the same functions. On the other hand, we show that the radii of univalence of some normalized Struve and Lommel functions are exactly the radii of starlikeness of the same functions. In addition, by using some ideas of Ismail and Muldoon we present some new lower and upper bounds for the zeros of derivatives of some normalized Struve and Lommel functions. The Laguerre-Pólya class of real entire functions plays an important role in our study.

Aktaş, Ibrahim; Orhan, Halit

In the present investigation our main aim is to give lower bounds for the ratio of some normalized q-Bessel functions and their sequences of partial sums. Especially, we consider Jackson's second and third q-Bessel functions and we apply one normalization for each of them.

Aktaş, Ibrahim; Baricz, Árpád; Yaǧmur, Nihat

Tight lower and upper bounds for the radii of univalence (and starlikeness) of some normalized Bessel, Struve and Lommel functions of the first kind are obtained via Euler-Rayleigh inequalities. It is shown also that the radius of univalence of the Struve functions is greater than the corresponding radius of univalence of Bessel functions. Moreover, by using the idea of Kreyszig and Todd, and Wilf it is proved that the radii of univalence of some normalized Struve and Lommel functions are exactly the radii of starlikeness of the same functions, and they are actually solutions of some functional equations. The Laguerre-Pólya class of entire functions plays an important role in our study.

Aktaş, İbrahim; Baricz, Árpád

In this paper the radii of starlikeness of Jackson’s second and third q-Bessel functions are considered and for each of them three different normalization are applied. By applying Euler–Rayleigh inequalities for the first positive zeros of these functions tight lower and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre–Pólya class of real entire functions plays an important role in this study. In particular, we obtain some new bounds for the first positive zero of the derivative of the classical Bessel function of the first kind.