Kolmogorov type inequalities for the Marchaud fractional derivatives on the real line and the half-line

In this paper we establish some new Kolmogorov type inequalities for the Marchaud and Hadamard fractional derivatives of functions defined on a real axis or semi-axis. Simultaneously we solve two related problems: the Stechkin problem on the best approximation of unbounded operators by bounded ones on a given class of elements and the problem of optimal recovery of operator on elements from some class given with prescribed error. Keywords: inequalities for derivatives, fractional derivatives, approx- imation of unbounded operators by bounded ones, optimal recovery of operators, ideal lattice.Comment: 3 figure

Comparison of Morphology and Cytotoxicity of Cellulose Composites with Nano- and Microhydroxyapatite for Bone Tissue Engineering

Scaffolds for bone tissue regeneration must be precisely designed as they support cell attachment, proliferation, differentiation and blood vessel in-growth. Moreover, the materials which are implanted in human body must be non-cytotoxic, absolutely harmless. In this work cellulose scaffolds with nanohydroxyapatite and microhydroxyapatite were prepared. The results obtained in this work revealed that the morphology of the scaffolds depended on the size of hydroxyapatite particles. The porosity of the scaffolds varied from 66 to 72%. The pores were interconnected with the average diameter 0.49 and 0.54 mm for scaffolds with nano- and microhydroxyapatite, respectively. Biocompatibility and potential toxicity of the experimental cellulose/hydroxyapatite scaffolds were tested. It was determined that the scaffolds containing nanohydroxyapatite particles showed slight cytotoxic effect

Using of the Agglomeration-in-liquid for the Technology of the Fine Materials

The content of the fine and ultrafine particles in the raw material results in difficulty of the separation, the loss of the valuable components and ecological contamination. Secondary using of the fine particles is impossible without their granulation. This problem has been solved by the agglomeration-in-liquid method. An agglomeration-in-liquid method is a process to produce agglomerates in a liquid phase from solid particles suspended in the liquid. The surface of solid particles and the binding liquid must be of identical polarity, but the continuous phase must be of the opposite polarity. The water solutions of the surfactant are the binding liquids or the organic liquids