‎Some improvements of Young inequality and its reverse for positive‎ ‎numbers with Kantorovich constant $K(t‎, ‎2)=frac{(1+t)^2}{4t}$‎ ‎are given‎. ‎Using these inequalities some operator inequalities and‎ ‎Hilbert-Schmidt norm versions for matrices are proved‎. ‎In‎ ‎particular‎, ‎it is shown that if $a‎, ‎b$ are positive numbers and‎ ‎$0 leqslant nu leqslant 1,$ then for all integers $ kgeqsl...

Inthis paper, the main aim is to introduce the class $mathcal{U}_p(lambda,alpha,beta,k_0)$ of $p$-harmonic mappings togetherwith its subclasses $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p$ and $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p^0$, andinvestigate the properties of the mappings in these classes. First,we give a sufficient condition for mappings to be in $mathcal{U}_p(l...

‎we obtain the asymptotic expansion of the sequence with general term $frac{a_n}{g_n}$‎, ‎where $a_n$ and $g_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎also‎, ‎we obtain some explicit bounds concerning $g_n$ and $frac{a_n}{g_n}$.

The filamentous, heterocyst-forming cyanobacteria perform oxygenic photosynthesis in vegetative cells and nitrogen fixation in heterocysts, and their filaments can be hundreds of cells long. In the model heterocyst-forming cyanobacterium Anabaena sp. strain PCC 7120, the genes in the fraC-fraD-fraE operon are required for filament integrity mainly under conditions of nitrogen deprivation. The f...

Red dish mud-rich sed i ments are com mon in sev eral karst ar eas, in the form of red sur face soils and clastic cave in fill ings. The or i gin and sig nif i cance of red sur face soils have been much de bated over re cent years, while clastic mud-rich sed i ments in cave en vi ron ments have re ceived less at ten tion from geoscientists. The ge netic re la tion ship be tween these two ma te ...

Inverse Young inequality asserts that if $nu >1$, then $|zw|ge nu|z|^{frac{1}{nu}}+(1-nu)|w|^{frac{1}{1-nu}}$, for all complex numbers $z$ and $w$, and equality holds if and only if $|z|^{frac{1}{nu}}=|w|^{frac{1}{1-nu}}$. In this paper the complex representation of quaternion matrices is applied to establish the inverse Young inequality for matrices of quaternions. Moreover, a necessary and ...

BACKGROUND Rattan tea is a medicinal plant that has been used for many years for the treatment of inflammation, fatty liver, tumor, diabetes, and hyperlipidemia. OBJECTIVE A green and novel approach based on surfactant-mediated, ultrasonic-assisted extraction (SM-UAE) was developed for the extraction of antioxidant polyphenols from Rattan tea. A nonionic surfactant Tween-80 was selected as ex...

Sao Paulo Med J. 2007;125(3):132-8. O R IG IN A L A R T IC L E João Carlos Belloti João Baptista Gomes dos Santos Álvaro Nagib Atallah Walter Manna Albertoni Flavio Faloppa Fractures of the distal radius (Colles’ fracture) Universidade Federal de São Paulo — Escola Paulista de Medicina (Unifesp-EPM), São Paulo, Brazil CONTEXT AND OBJECTIVE: �������� �������� frac��r� i� a c�mm�n c�inica� �i��a�...