Negative Sobolev Spaces in the Cauchy Problem for the Cauchy-Riemann Operator

Let D be a bounded domain in Cn (n > 1) with a smooth boundary @D. We indicate appropriate Sobolev spaces of negative smoothness to study the non-homogeneous Cauchy problem for the Cauchy-Riemann operator @ in D. In particular, we describe traces of the corresponding Sobolev functions on @D and give an adequate formulation of the problem. Then we prove the uniqueness theorem for the problem, describe its necessary and sufficient solvability conditions and produce a formula for its exact solution

New data on biology of siberian cisco <i>Coregonus sardinella</i> (Coregonidae) from the Anadyr River

The data on biology of siberian cisco were collected during its spawning migration in the middle stream of the Anadyr River in September-October of 2010-2011 and during the feeding of mature fish in the Anadyr estuary in June-August of 2011. Besides, the data collected previously in 1987 and 1992 were processed with modern research techniques. The bulk of spawning lake-river cisco is the fish of the age 5+ years with the length 206-218 mm and weight 81-103 g; the feeding cisco in the estuary has mainly the age 4-6+ years, mean length 233.0 ± 4.4 mm and mean weight 119 ± 11 g. Cisco females are larger than males: the maximum size of females is 255 mm with the weight 167 g (age 7+) and the maximum size of males is 249 mm with the weight 160 g (age 7+). Modern age structure of spawning cisco is rejuvenated comparing with that in 1987 and 1992: the maximum age of cisco is now 3 years less, and the average age is 1 year less. The portions of large-sized and medium-sized mature fish became less, too, as well as the average length and weight became 36 mm and 78 g less for females, and 30 mm and 47 g less for males. Recently only 6 age groups of cisco spawn (from 3+ to 8+, mainly 5-6-years) whereas its 8 age groups spawned in the 1980s (from 4+ to 11+, with the modal age 5-8 years). The size decreasing could be partially explained by its higher abundance in recent years and relatively low summer discharge of the Anadyr in 2005-2010. Linear growth of spawning cisco has high rate in the first 5 years, reduces in the 6th year, and decreases abruptly in the 7th year; the growth rate of the lake-river cisco is generally lower than that of the estuarine cisco. Annual linear increments of immature cisco increase significantly in the next year after large runs of chum salmon, but not in a year of large run. The lake-river cisco is an important object of local fishery, with the main fishing grounds at Markovo where it is caught in autumn during its mass spawning migration. Annual landings of cisco are very variable, with significant decreasing in the 2000s. Modern state of the lake-river cisco population is determined mainly by hydrological regime of the river and strength of the chum salmon runs

Waveguide-saturable absorber fabricated by femtosecond pulses in YAG:Cr4+ crystal for Q-switched operation of Yb-fiber laser

A waveguide-saturable absorber with low propagation loss is fabricated by femtosecond pulses in YAG:Cr4+ crystal. Q-switch operation of a Yb fiber laser with the new saturable absorber having absorption saturation parameters similar to the bulk YAG:Cr4+ crystal is demonstrated

Lawson criterion for ignition exceeded in an inertial fusion experiment

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion

Negative Sobolev Spaces in the Cauchy Problem for the Cauchy-Riemann Operator

Let D be a bounded domain in Cn (n > 1) with a smooth boundary @D. We indicate appropriate Sobolev spaces of negative smoothness to study the non-homogeneous Cauchy problem for the Cauchy-Riemann operator @ in D. In particular, we describe traces of the corresponding Sobolev functions on @D and give an adequate formulation of the problem. Then we prove the uniqueness theorem for the problem, describe its necessary and sufficient solvability conditions and produce a formula for its exact solution