On compactness of Laplace and Stieltjes type transformations in Lebesgue spaces

We obtain criteria for integral transformations of Laplace and Stieltjes type to be compact on Lebesgue spaces of real functions on the semiaxis

On estimates of Schatten-von Neumann norms of Hardy-Steklov operator

Upper and lower estimates are obtained for the Schatten-von Neumann norms of the Hardy-Steklov operator in Lebesgue function spaces on the semi-axis

Photoluminescence of Lead Sulfide Quantum Dots of Different Sizes in a Nanoporous Silicate Glass Matrix

The optical properties of lead sulfide quantum dots (QDs) of different sizes embedded in a nanoporous silicate glass matrix (NSM) are investigated by steady-state and transient photoluminescence spectroscopy. The use of this matrix allows the fabrication of samples with reproducible optical characteristics, for both isolated and close-packed QDs. Low-temperature PL analysis of isolated QDs with sizes of 3.7 and 4.5 nm shows that the coefficient of temperature shift of the PL position changes sign with reducing QD size because of size-dependent contributions from thermal expansion, mechanical strain, and electron–phonon coupling. The PL intensity is determined by size-dependent splitting of the lowest energy electronic state

Diabetes mellitus type 1 in adults

Public organization “Russian Association of Endocrinologists”. Clinical guidlines

Diabetes mellitus type 2 in adults

Public organization “Russian Association of Endocrinologists”. Clinical guidelines.&nbsp

On boundedness and compactness of a certain class of kernel operators

New conditions for Lp[0,∞)-Lq[0,∞) boundedness and compactness (1<p, q<∞) of the map f→w(x)∫a(x)b(x)k(x,y)f(y)v(y)dy with locally integrable weight functions v,w and a positive continuous kernel k(x,y) from the Oinarov’s class are obtained

Hardy operator with variable limits on monotone functions

We characterize weighted Lp-Lq inequalities with the Hardy operator of the form Hf(x)=∫a(x)b(x)f(y)u(y) dy with a non-negative weight function u, restricted to the cone of monotone functions on the semiaxis. The proof is based on the Sawyer criterion and the boundedness of generalized Hardy operator with variable limits