Three realizations of the quantum affine algebra <Emphasis Type="Italic">U</Emphasis><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript>(<Emphasis Type="Italic">A</Emphasis><Subscript>2</Subscript><Superscript>(2)</Superscript>

We establish explicit isomorphisms between three realizations of the quantum twisted affine algebra U _q (A ₂ ⁽²⁾: the Drinfeld current realization, the Chevalley realization, and the so-called RLL realization proposed by Reshetikhin, Takhtajan, and Faddeev.     

Impurity-induced coherent current oscillations in one-dimensional conductors

The electronic transport through a single impurity in a repulsive Luttinger liquid (LL) has been theoretically studied. It has been found that the direct current Ī above the threshold voltage related to the strength of the impurity potential is accompanied by coherent oscillations with frequency f= Ī/e. There is an analogy with the Josephson junctions: the well-known regime of the power-law I−V curves in the LL corresponds to the damping of the Josephson current below the critical one, while the oscillatory regime in the LL can be compared with the Josephson oscillations above the critical current. The text was submitted by the authors in English.     

Numerical reconstruction stability of fiber Bragg gratings

Traditional algorithms for solving the inverse scattering problem for a fiber Bragg grating are described, and a new numerical method for this problem is developed. The method is based on the fast inversion of a matrix using its Toeplitz symmetry and on a special “inner-bordering” procedure. It is shown that the method is equally efficient as the well-known discrete layer peeling method but exceeds the latter in accuracy, especially for high-reflectance gratings. The stability of the proposed method with respect to initial data errors is demonstrated.     

Population transfer between two quantum states by piecewise chirping of femtosecond pulses: theory and experiment

We propose and experimentally demonstrate the method of population transfer by piecewise adiabatic passage between two quantum states. Coherent excitation of a two-level system with a train of ultrashort laser pulses is shown to reproduce the effect of an adiabatic passage, conventionally achieved with a single frequency-chirped pulse. By properly adjusting the amplitudes and phases of the pulses in the excitation pulse train, we achieve complete and robust population transfer to the target state. The piecewise nature of the process suggests a possibility for the selective population transfer in complex quantum systems.     

Inverse scattering for the one-dimensional Helmholtz equation: fast numerical method

The inverse scattering problem for the one-dimensional Helmholtz wave equation is studied. The equation is reduced to a Fresnel set that describes multiple bulk reflection and is similar to the coupled-wave equations. The inverse scattering problem is equivalent to coupled Gel'fand-Levitan-Marchenko integral equations. In the discrete representation its matrix has T?plitz symmetry, and the fast inner bordering method can be applied for its inversion. Previously the method was developed for the design of fiber Bragg gratings. The testing example of a short Bragg reflector with deep modulation demonstrates the high efficiency of refractive-index reconstruction.     

Powder diffraction from a continuous microjet of submicrometer protein crystals

Atomic‐resolution structures from small proteins have recently been determined from high‐quality powder diffraction patterns using a combination of stereochemical restraints and Rietveld refinement [Von Dreele (2007), J. Appl. Cryst. 40 , 133–143; Margiolaki et al. (2007), J. Am. Chem. Soc. 129 , 11865–11871]. While powder diffraction data have been obtained from batch samples of small crystal‐suspensions, which are exposed to X‐rays for long periods of time and undergo significant radiation damage, the proof‐of‐concept that protein powder diffraction data from nanocrystals of a membrane protein can be obtained using a continuous microjet is shown. This flow‐focusing aerojet has been developed to deliver a solution of hydrated protein nanocrystals to an X‐ray beam for diffraction analysis. This method requires neither the crushing of larger polycrystalline samples nor any techniques to avoid radiation damage such as cryocooling. Apparatus to record protein powder diffraction in this manner has been commissioned, and in this paper the first powder diffraction patterns from a membrane protein, photosystem I, with crystallite sizes of less than 500 nm are presented. These preliminary patterns show the lowest‐order reflections, which agree quantitatively with theoretical calculations of the powder profile. The results also serve to test our aerojet injector system, with future application to femtosecond diffraction in free‐electron X‐ray laser schemes, and for serial crystallography using a single‐file beam of aligned hydrated molecules.     

Simulations of Microbial-Enhanced Oil Recovery: Adsorption and Filtration

In the context of microbial-enhanced oil recovery (MEOR) with injection of surfactant-producing bacteria into the reservoir, different types of bacteria attachment and growth scenarios are studied using a 1D simulator. The irreversible bacteria attachment due to filtration similar to the deep bed filtration (DBF) is examined along with the commonly used reversible equilibrium adsorption (REA). The characteristics of the two models are highlighted. The options for bacteria growth are the uniform growth in both phases and growth of attached bacteria only. It is found that uniform growth scenario applied to filtration model provides formation of two oil banks during recovery. This feature is not reproduced by application of REA model or DBF with growth in attached phase. This makes it possible to select a right model based on the qualitative analysis of the experimental data. A criterion is introduced to study the process efficiency: the dimensionless time at which average recovery between pure water injection and maximum surfactant effect is reached. This characteristic recovery period (CRP) was studied as a function of the different MEOR parameters such as bacterial activity, filtration coefficients, and substrate injection concentrations. For both growth scenarios, there is a zone of optimal activity at which the CRP is minimal. Dependence of the CRP on substrate concentration for uniform growth scenario has also an optimal zone. Therefore, growth rate and the substrate concentration should be above a certain threshold value and still not be too high to obtain the minimum CRP. On the other hand, no such zone was found if the bacteria could grow only in the attached phase. Dependencies on both the injected concentration and filtration coefficient are monotonous in this case.     

Extending Solutions of Holomorphic Partial Differential Equations Across Real Hypersurfaces

The main result in this paper, Theorem 1.2, generalizes a theoremof Zerner [26] concerning sufficient conditions for the holomorphiccontinuability of a solution of a linear holomorphic partialdifferential equation across a point of a hypersurface, on oneside of which it is holomorphic. The point of the new theoremis, roughly speaking, that it applies also to regular solutionsof partial differential equations whose coefficients may havecertain kinds of singularities. This enables us to deduce somenew results (see 2) on elliptic partial differential equationsin R²:Theorem 2.1 extends a result of Vekua on the size of thedomain of holomorphy of solutions to elliptic equations, inthe case where singularities are permitted in the coefficients;Theorem 2.2 is of an apparently novel type, showing (roughly)that under certain conditions the solution to Cauchy's problemis real-analytic in a domain whose size depends only on theprincipal part of the operator, which is assumed to be the Laplacian,and the Cauchy data on the real axis. (Results of this kindare very delicate, as we shall illustrate in 4 with a simplecounterexample.) Theorem 2.2 is new and non-trivial even forequations with analytic coefficients, in which case though,Theorem 1.2 is not needed for the proof.     

On the outputs of linear control systems

This paper studies autonomous, single-input, single-output linear control systems on finite time intervals. The object of interest is the output operatorO, which associates to each input function and initial state vector the corresponding system output. Main result: If the system has relative degree r<∞, then for any “admissible” Banach space U of inputs, O is a bounded operator taking U×Cn onto the “Sobolev space” of complex functions f∈C(r−1)([0,T]) for which the (r−1)-order derivative f(r−1) is absolutely continuous, with f(r)∈U. This completes recent results of Jönsson and Martin [Ulf Jönsson, Clyde Martin, Approximation with the output of linear control systems, J. Math. Anal. Appl. 329 (2007) 798-821] who showed that if the system is minimal and U is either L²([0,T]) or C([0,T]), then has dense range.     

Reactions of the paramagnetic quaternary Mannich base in an alkaline medium

The catalytic action of aqueous NaOH at 20 °C on 2,2,6,6-tetramethyl-3-(N-methyl-piperidiniomethyl)-4-oxopiperidine 1-oxyl iodide rapidly resulted in the formation (k = 57 L mol⁻¹ s⁻¹) of a paramagnetic ketone with an activated double bond: 2,2,6,6-tetramethyl-3-methylidene-4-oxopiperidine 1-oxyl. The latter underwent slow transformation into a nitroxyl biradical containing an activated double bond and a methylene bridge linking positions 3 and 3′. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 421–423, February, 2008.