Global exact controllability in infinite time of Schrödinger equation

In this paper, we study the problem of controllability of Schrödinger equation. We prove that the system is exactly controllable in infinite time to any position. The proof is based on an inverse mapping theorem for multivalued functions. We show also that the system is not exactly controllable in finite time in lower Sobolev spaces.     

Investigation of condensed pyrimidine,pyrazine, and pyridine systems

The reaction of 5-hydroxy-6-aminopyrimidines with chloromalonic ester in alcohol or with bromomalonic ester in dimethylformamide leads to 6-carbethoxypyrimido-7-oxazinones, whereas a mixture of 6-carbethoxypyrimido-7-oxazinones and 6,6-spirodipyrimido-7-oxazinones is formed in the reaction with bromomalonic ester in alcohol. The latter oxazinones were obtained by reaction of 5-hydroxy-6-aminopyrimidines with dibromomalonic ester. Some of the properties of the synthesized compounds were studied.See [1] for communication XXV.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 391–396, March, 1978.     

One-Step Three-Component Synthesis of New 2,5,6,7-Functionalized 5,8-Dihydropyrido-[2,3-<Emphasis Type="Italic">d</Emphasis>]pyrimidin-4(3<Emphasis Type="Italic">H</Emphasis>)-ones

One-step three-component cyclocondensation of 2,6-disubstituted pyrimidin-4(3H)-ones with 1,3-dicarbonyl compounds and some aromatic and heterocyclic aldehydes on heating or under microwave irradiation afforded new functionally substituted 5,8-dihydropyrido[2,3-d]pyrimidin-4(3H)-ones. Conventional heating was found to be more advantageous. The effects of the 2-substituent in the initial pyrimidin-4(3H)-one and the nature of the dicarbonyl component on the product structure and yield were analyzed.     

Polynomial mixing for the complex Ginzburg–Landau equation perturbed by a random force at random times

In this paper we study the problem of ergodicity for the complex Ginzburg–Landau (CGL) equation perturbed by an unbounded random kick-force. Randomness is introduced both through the kicks and through the times between the kicks. We show that the Markov process associated with the equation in question possesses a unique stationary distribution and satisfies a property of polynomial mixing.      

New Bis-4H-1,2,4-triazoles and Their In Vitro Study as DNA Methylation Inhibitors

Russian Journal of General Chemistry - Bis-1,2,4-triazoles with aryl and alkyl linkers were synthesized. In order to increase their hydrophilicity and potential biological activity, pharmacophore...     

On the existence of condensed phases in low-dimensional systems

It is shown that the threshold interaction constant (TIC) α_D for the existence of a condensed phase increases with the dimension D of a Bose system (α₃ < α₂ < α₁). TICs are evaluated exactly for a wide class of two-parameter potentials (the latter may approximate real physical interactions). The results are applied to spin-polarized systems. The possibility of an electric field induced liquid-gas transition is discussed. The TIC for N-particle clusters diminishes with N.     

Effect of a local perturbation in a fermionic ladder

We study the effect of a local external potential on a system of two parallel spin-polarized nanowires placed close to each other. For single-channel nanowires with repulsive interaction we find that transport properties of the system are highly sensitive to the transverse gradient of the perturbation: the asymmetric part completely reflects the electrons leading to vanishing conductance at zero temperature, while the flat potential remains transparent. We envisage a possible application of this unusual property in the sensitive measurement of local potential field gradients.     

Semi-global weak stabilization of bilinear Schrödinger equations

We consider a linear Schrödinger equation, on a bounded domain, with bilinear control, representing a quantum particle in an electric field (the control). Recently, Nersesyan proposed explicit feedback laws and proved the existence of a sequence of times ${(t_n)}_{n\in \mathbb{N}}$ for which the values of the solution of the closed loop system converge weakly in $H^2$ to the ground state. Here, we prove the convergence of the whole solution, as $t\to +\infty$. The proof relies on control Lyapunov functions and an adaptation of the LaSalle invariance principle to PDEs.