A necessary and sufficient condition for differentiability of integrals of random measures in Rn over n-dimensional intervals

Translated from Matematicheskie Zametki, Vol. 49, No. 4, pp. 63–68, April, 1991.     

On Exponential Summability of Rectangular Partial Sums of Double Trigonometric Fourier Series

In this paper, we study the a.e. exponential strong summability problem for the rectangular partial sums of double trigonometric Fourier series of functions in L logL.     

Everywhere divergent Φ-means of Fourier series

For a function ? ∈, L ¹( $\mathbb{T}$ ), we investigate the sequence (C, 1) of mean values Φ(¦S _k (x, ?) ? ?(x)¦), where Φ(t): [0, +∞) → [0,+∞), Φ(0) = 0, is a continuous increasing function. We prove that if Φ increases faster than exponentially, then these means can diverge everywhere. Divergence almost everywhere of such means was established earlier.     

Immobilization of Fungal β-Glucosidase on Silica Gel and Kaolin Carriers

β-Glucosidase is a key enzyme in the hydrolysis of cellulose for producing feedstock glucose for various industrial processes. Reuse of enzyme through immobilization can significantly improve the economic characteristics of the process. Immobilization of the fungal β-glucosidase by covalent binding and physical adsorption on silica gel and kaolin was conducted for consequent application of these procedures in large-scale industrial processes. Different immobilization parameters (incubation time, ionic strength, pH, enzyme/support ratio, glutaric aldehyde concentration, etc.) were evaluated for their effect on the thermal stability of the immobilized enzyme. It was shown that the immobilized enzyme activity is stable at 50 °C over 8 days. It has also been shown that in the case of immobilization on kaolin, approximately 95% of the initial enzyme was immobilized onto support, and loss of activity was not observed. However, covalent binding of the enzyme to silica gel brings significant loss of enzyme activity, and only 35% of activity was preserved. In the case of physical adsorption on kaolin, gradual desorption of enzyme takes place. To prevent this process, we have carried out chemical modification of the protein. As a result, after repeated washings, enzyme desorption from kaolin has been reduced from 75 to 20–25% loss.     

Divergence almost everywhere of rectangular partial sums of multiple fourier series of bounded functions

In this paper we establish the following results, which are the multidimensional generalizations of well-known theorems:

BMO-Estimation and Almost Everywhere Exponential Summability of Quadratic Partial Sums of Double Fourier Series

A \(\mathrm{BMO\,}\) -estimation for quadratic partial sums of two-dimensional Fourier series is proved from which is derived an almost everywhere exponential summability of quadratic partial sums of double Fourier series.     

On everywhere divergence of the strong Φ-means of Walsh–Fourier series

Almost everywhere strong exponential summability of Fourier series in Walsh and trigonometric systems was established by Rodin in 1990. We prove, that if the growth of a function Φ(t):[0,∞)→[0,∞)$\Phi (t):[0,\infty )\to [0,\infty )$ is bigger than the exponent, then the strong Φ-summability of a Walsh–Fourier series can fail everywhere. The analogous theorem for trigonometric system was proved before by one of the authors of this paper.     

On unbounded divergence sets of series in orthonormal bases

In this paper we establish a number of theorems providing complete characterizations of divergence sets of general series in orthogonal bases with a localization property.     

The Fatou Property for General Approximate Identities on Metric Measure Spaces

Mathematical Notes - Abstract approximate identities on metric measure spaces are considered in this paper. We find exact conditions on the geometry of domains for which the convergence of...