The alumina used for the present study was purchased from Union Carbide Corp. as Linde Alumina Polishing Powder Type A. X-ray diffraction and chemical analysis of the powder shows the mineral to be a well-crystallized corundum of high purity(>~ AlzOJ). Morphologically, the powder is constituted of micrometer-sized aggregates composed of smaller particles (between 200 and 500 nm). Nitrogen adsor...

In this paper, we prove the Hyers-Ulam stability in$beta$-homogeneous probabilistic modular spaces via fixed point method for the functional equation[f(x+ky)+f(x-ky)=f(x+y)+f(x-y)+frac{2(k+1)}{k}f(ky)-2(k+1)f(y)]for fixed integers $k$ with $kneq 0,pm1.$

Dünyadaki tüm topluluklar kendilerini yo?uran kültür ikliminden çevreye bakar ve o çevreyi anlamland?r?r. Topluluklar ve/veya milletler, özgün yapan ikliminin referanslar? ile dü?ünür, ya?ar gelece?i tasarlar. Milletler bu iklimi içerisinde ya?ad?klar? co?rafyay? de?erlendirirler. Fiziki co?rafyay?, çe?itli biçimlerde be?eri co?rafyaya dönü?türürler. Bu i?i, do?ay? dönü?türerek yapt?klar? gibi ...

in this paper, some results of singh, gopalakrishna and kulkarni (1970s) have been extended to higher order derivatives. it has been shown that, if $sumlimits_{a}theta(a, f)=2$ holds for a meromorphic function $f(z)$ of finite order, then for any positive integer $k,$ $t(r, f)sim t(r, f^{(k)}), rrightarrowinfty$ if $theta(infty, f)=1$ and $t(r, f)sim (k+1)t(r, f^{(k)}), rrightarrowinfty$ if $th...

In this paper, some results of Singh, Gopalakrishna and Kulkarni (1970s) have been extended to higher order derivatives. It has been shown that, if $sumlimits_{a}Theta(a, f)=2$ holds for a meromorphic function $f(z)$ of finite order, then for any positive integer $k,$ $T(r, f)sim T(r, f^{(k)}), rrightarrowinfty$ if $Theta(infty, f)=1$ and $T(r, f)sim (k+1)T(r, f^{(k)}), rrightarrowinfty$ if $Th...