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On the closedness, the self-adjointness and the normality of the product of two unbounded operators

Mortad M. H.

Demonstratio Mathematica

2012

Vol. 45, nr 1

161-167

Let A and B be two unbounded densely defined operators on a Hilbert space H . The purpose of this work is to give simple conditions that make the product AB closed, self-adjoint and normal provided the two operators are so.

On the radiocesium behavior in a small humic lake (Lithuania)

Tarasiuk N., Moisejenkova A., Koviazina E., Karpicz R., Astrauskiene N.

Nukleonika

2009

Vol. 54, No. 3

211-220

Peculiarities of radiocesium contamination of a small humic lake, which became meromictic some thirty-five years ago due to the inflow of a large amount of humic water, are presented. The lake consists of two separate water layers, which do not intermix. A lower water layer of the lake below some 3-m depth is stagnant and anaerobic, and radiocesium load of the sediments is mainly caused by nuclear weapons fallout. The radiocesium load of the sediments of the upper monomictic water layer is significantly larger due to additional contamination after the Chernobyl accident. Radiocesium activity concentrations in lake water increase with depth, and even in the surface layer, they are commonly the largest among the neighboring lakes with transparent water. It is shown that bottom areas of the monomictic part of the lake with the elevated radiocesium deepening into sediments are related to the favorite sites of the tench (Tinca tinca) winter torpor. Sediment bioturbation and redistribution due to tench activities distort naturally formed radiocesium vertical profiles and they cannot be used for estimations of sedimentation rates and sediment chronology. The studied lake can be useful as an analogous model in analyzing structural and radiological consequences of humic water inflows to closed lakes. Concerning extreme radiological situations in closed humic lakes related to their specific vertical structure, they may be treated as critical objects in assessing the risk to humans after radionuclide deposition events.