Inequalities of Young-type

Necessary and sufficient conditions are given for the Young-type inequalityxyf(x)+g(y) (x, y>0) to hold wheref, g are arbitrary real functions on the positive half line.     

Thermal analysis of complexes of cadmium chloride picoline

The thermal decomposition of the, and- picoline complexes of cadmium were studied by means of TG-DTG-DTA. In connection with the preparation of the complex compounds, it was established that the ligand number was influenced by the reaction medium. The thermal decomposition took place stepwise, and intermediates were formed which could be isolated with a derivatograph by the freezing-in method. The structures and properties of these previously unknown compounds were investigated by far-IR spectroscopy and X-ray powder diffraction.

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Zusammenfassung Der thermische Zersetzungsprozess der Komplexverbindungen von Cadmiumchlorid mit-, - oder-Picolin wurde durch simultane TG-DTG-DTA im Derivatograph untersucht. Die Ligandenzahl der Komplexverbindungen wird durch das Reaktionsmedium bei der Präparation beeinflusst. Die thermische Zersetzung erfolgt stufenweise, Zwischenprodukte konnten mittels Derivatograph durch die Einfriermethode isoliert werden. Struktur und Eigenschaften dieser bisher unbekannten Verbindungen wurden durch Fern-IR-Spektroskopie und Röntgenpulverbeugung untersucht.

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On the equality of two-variable general functional means

Aequationes mathematicae - Given two functions $$f,g:I\rightarrow \mathbb {R}$$ and a probability measure $$\mu $$ on the Borel subsets of [0, 1], the two-variable mean $$M_{f,g;\mu...     

Special Simultaneous Quasi-uniform Extensions

A necessary and sufficient condition is presented for the existence of a quasi-uniformity for a prescribed topology, such that the quasi-uniformity is transitive, doubly uniformly strict and uniformly regular, respectively.     

Measurable solutions of a (2, 2)-type sum form functional equation

Summary In this paper we find the general measurable solutions of the functional equationF(xy) + F(x(1 – y)) – F((1 – x)y) – F((1 – x)(1 – y)) = G(x)H(y) (x, y ]0, 1[) whereF, G, H:]0, 1[ C are unknown functions. The solution of this equation is part of our program to determine the measurable solutions of the functional equationF ₁₁ (xy) + F ₁₂ (x(1 – y)) + F ₂₁ ((1 – x)y) + F ₂₂ ((1 – x)(1 – y)) = G(x)H(y) (x, y ]0, 1[). Our method of solution is based on the structure theorem of sum form equations of (2, 2)-type and on a result of B. Ebanks and the author concerning the linear independence of certain functions.     

Subhomogene Mittelwerte

Ohne Zusammenfassung