Unitary correlation in nuclear reaction theory

We prove that the amplitudes for the (d,p), (d,pn) and (e,e'p) reactions determining the asymptotic behavior of the exact scattering wave functions in the corresponding channels are invariant under unitary correlation operators while the spectroscopic factors are not. Moreover, the exact reaction amplitudes are not parametrized in terms of the spectroscopic factors and cannot provide a tool to determine the spectroscopic factors.Comment: 5 page

Productivity of corn hybrids in relation to the seeding rate

ArticlePotential yield of corn hybrids with a different FAO number is limited by not only rainfall amount, average soil and air temperature throughout vegetation period, but also directly depends on plant density. The study and practical application of special agricultural techniques allows us to limit and mitigate the negative impact of these factors on the productivity of maize, depending on the indicators under study and the soil and climatic resources of the cultivation zone. Therefore, the study of the influence of the seeding rate on the growth and development of corn plants remains relevant. The results presented make it possible to choose optimal seeding rates for corn hybrids of early and middle groups of ripeness (FAO 180-280). Overcrowding from 61,000 to 93,000 seeds ha-1 leads to increase in interstage period 'sprouting–wax ripeness' of Rodnik 179SV hybrid for 4 days, of MAS 12R and AMELIOR hybrids–for 2 days, and of MAS 30K hybrid – for 3 days. Hybrids Rodnik 179SV and AMELIOR reached maximum height – 217 cm and 214 cm respectively – at seeding rate of 73,000 seeds ha-1 , while hybrids MAS 12R and MAS 30K grew up to their 213 cm and 223 cm respectively at seeding rate of 77,000 seeds ha-1 . Decrease in seeding rate to less than 73,000 seeds ha-1 and, contrary to it, overcrowding of seeds of more than 77,000 seeds ha-1 leads to decrease in corn hybrid plant height. Agronomically, the most efficient for maximizing early ripe Rodnik 179SV and MAS 12R hybrids yields (6.39 and 6.73 t ha-1 ) and middle-early ripe AMELIOR hybrid yield (6.81 t ha-1 ) was the seeding rate of 73,000 seeds ha-1 , while the highest yield of middle MAS 30K hybrid (7.21 t ha-1 ) was at the seeding rate of 77,000 seeds ha-1

Escape of mass and entropy for diagonal flows in real rank one situations

Let G be a connected semisimple Lie group of real rank 1 with finite center, let be a non-uniform lattice in G and a any diagonalizable element in G. We investigate the relation between the metric entropy of a acting on the homogeneous space \G and escape of mass. Moreover, we provide bounds on the escaping mass and, as an application, we show that the Hausdorff dimension of the set of orbits (under iteration of a) which miss a fixed open set is not full

The leading asymptotic terms of the three-body Coulomb scattering wave function

The asymptotic wave function derived by Alt and Mukhamedzhanov [Phys. Rev. A 47, 2004 (1993)] and Mukhamedzhanov and Lieber [Phys. Rev. A 54, 3078 (1996)] has been refined in the region where the pair $(\beta,\gamma)$ remains close to each other while the third particle $\alpha$ is far away from them $(\rho_{\alpha} \to \infty$, $r_{\alpha}/\rho_{\alpha}\to 0)$. The improved wave function satisfies the Schr\"odinger equation up to the terms of order $O(1/{\rho_{\alpha}}^{3})$, provides the leading asymptotic terms of the three-body scattering wave function with Coulomb interactions and gives further insight into the continuum behavior of the three-charged-particle wave function and helps to obtain $3\to 3$ scattered wave. This opens up further ways of solving and analysing the three-body Schr\"odinger equation by numerical means

Simulation of a High-Frequency Link of Phase Comparison Protection of Transmission Lines for Optimization its Settings

The objective of this work is to determine the influence of high-frequency link (HFL) on functioning of phase comparison protection (PCP) through the usage of detailed models that take into account specific features of the PCP and processes in HFL. The article describes the case of the most common variant of the high frequency signal transmission by using a scheme 'phase-to-ground'. To verify suggested solution the developed mathematical model of HFL has been studied. Presented simulation results confirm the effectiveness of the proposed approach for solving the problem