We consider an inverse problem for a one-dimensional heat equation with involution and with periodic boundary conditions with respect to a space variable. This problem simulates the process of heat propagation in a thin closed wire wrapped around a weakly permeable insulation. The inverse problem consists in the restoration (simultaneously with the solution) of an unknown right-hand side of the equation, which depends only on the spatial variable. The conditions for redefinition are initial and final states. Existence and uniqueness results for the given problem are obtained via the method of separation of variables.

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The 'landscape mosaic' hypothesis predicts that adult male capercaillie Tetrao urogallus track available habitat when making distinct seasonal migrations. We tested this hypothesis by comparing movement from leks to summer range in three geographical regions, viz. northwest Russia (Pechora), southwest Russia (Tver) and southeast Norway (Varaldskogen). All radio-collared males dispersed out of their daytime lek territories to an average distance of 2.3 km (±0.37) from lek centres (N = 52). In Russia, three birds, which were not included in this estimate, moved beyond the 6-7 km detection distance, but returned the fol lowing year. Due to large variation among birds at each lek, the only signifi cant difference in movement was found between the birds at the lek in Pechora ( x = 1.3 km) and those at one of the two leks in Tver (x = 3.6 km) and at one of the three leks in Norway (x = 3.2 km). At all leks except the one in Tver, the amount of suitable summer habitat, e.g. old Norway spruce Picea abies forest on rich soil, was smaller within a 1-km radius of leks centres than in the outer two 1-km zones. Despite a large proportion of old spruce forest at and near the lek site in Tver, the males at this site moved >2 km from the lek centre in late May/early June. When data were pooled, the dispersal distance did not correlate with the amount of old spruce forest nor with the size of patch es (e.g. grain size) with increasing distance from leks. However, at the Nor wegian study area, which is highly fragmented with a fine-grained habitat mosa ic due to commercial forestry, variation in topography and soil quality, birds tended to move farther away from the leks with increasing patch size and with increasing proportion of old spruce forest. When fitting a second polynomi al regression function to the pooled data, there was only a weak relationship between dispersal distance and grain size for leks (P = 0.19). When includ ing all birds, the relationship was highly significant (P = 0.002). The Pechora lek in northwest Russia contributed mainly to the lack of a clear relationship between movement pattern and distribution of old spruce forest. Here large, contiguous bands of old spruce forest were located along the main river courses in a coarse-grained fashion within 2 km of lek sites. Thus, local con figuration of preferred summer habitat at the landscape scale probably affects both direction and movement to a larger extent than predicted from the 'land scape mosaic' hypothesis.

Relationships between number of eggs ( N g ) , brood weight ( arid body length (L) :mi n-cight, (MI) of females were studied for 16 orders and suborders of Crustacea. The study was based on the aathors' observations in the inland waters of the EinopeanUSSR, in the coastal regions of the farrnstern and northern seas nnd data from V. V. KUZNETSOV (preserved in archives). An cxtcnsirr literature wits also used. The equations describing the relationships (1Yg -f(L) and If$ = f ( TI-) arc calculated for some species and high taxons. On the average for the superclass (excluding the order Notostracn) the W,/W ratio appeared to bc 0.16. This ratio is markedly different for species of ?u'otost,rwa. It is supposed that t,liis difference is due to the high metabolic rate of Xot#ostraca.

Comparison of the number of species and biomass of planktonic crustaceans with morphometric. hydrological, and hydrochemical features of lakes in the zone of temperate climate shows that there are no functional correlations between the development of zooplankton and each of the other separate factors. Results of multiple regression analysis for description of relationships between biotic and abiotic conditions were unsatisfactory ( R J s 0 . 7 ) for the greater part of studies. It is apparently necessary to find methods to examine environmental characteristics limiting biological productivity in lakes and to classify lakes on this basis. Such classification may allow to work out quantitative predictions of plankton and benthos biomass development in response to change of some environmental factors.