Duality principle for discrete linear inclusions

Two properties of finite sets {Aj} of n x n-matrices are introduced: P-stability and BV-stability. These properties can be interpreted as two kinds of robustness of orbits of the form xi+1 = Ajixi + ui with respect to disturbances {ui}. Duality between these properties is established, which proves that they are equivalent, respectively, to the right convergent product (RCP) property and the left convergent product (LCP) property of finite sets of matrices. The results can be applied, in particular, in the theory of polyhedral Skorokhod problems and sweeping processes with oblique reflection

Lipschitz continuity of polyhedral Skorokhod maps

We show that a special stability condition of the associated system of oblique projections (the so-called ℓ-paracontractivity) guarantees that the corresponding polyhedral Skorokhod problem in a Hilbert space X is solvable in the space of absolutely continuous functions with values in X. If moreover the oblique projections are transversal, the solution exists and is unique for each continuous input and the Skorokhod map is Lipschitz continuous in both C([0,T]; X) and W1,1(0,T; X). An explicit upper bound for the Lipschitz constant is derived

Dynamic Speckle Interferometry of Thin Biological Objects: Theory, Experiments, and Practical Perspectives

Relation between the phase dynamics of the waves sounding thin biological object and the dynamics of the speckles in the object image plane was theoretically detected using a model dealing with interference of multiple waves with random phases. Formulas determining the dependence of time‐average intensity I ˜and temporal autocorrelation function η=η(t) of this intensity at a point of the image plane with mean value 〈x〉, mean square deviation σu, and correlation time τ0 of the difference between the optical paths ∆u of the wave pairs in the neighborhood of a conjugate point of the object plane were obtained. A relation between a normalized temporal spectral function of stationary process ∆u(t) and a temporal spectral radiation intensity fluctuation function was substantiated. An optical device relevant to the model used in the theory was developed. Good quantitative coincidence between the theory and the experiment was shown by means of dosed random variation of path difference ∆u. The calibration procedure for the device determining σu was developed; errors and the sensitivity limit of the technique were assessed. Application of value σu as a cell activity parameter on biological objects, namely, a monolayer of live cells on a transparent substrate in a thin cuvette with the nutrient solution was substantiated. It was demonstrated that the technique allows determination of herpes virus in the cells as early as 10 min from the experiment start. A necessity to continue upgrading of the technique was pointed out as well as its prospects for studying the cell reaction to toxic substances, bacteria, and viruses considered

The EROP-Moscow oligopeptide database

Natural oligopeptides may regulate nearly all vital processes. To date, the chemical structures of nearly 6000 oligopeptides have been identified from >1000 organisms representing all the biological kingdoms. We have compiled the known physical, chemical and biological properties of these oligopeptides—whether synthesized on ribosomes or by non-ribosomal enzymes—and have constructed an internet-accessible database, EROP-Moscow (Endogenous Regulatory OligoPeptides), which resides at . This database enables users to perform rapid searches via many key features of the oligopeptides, and to carry out statistical analysis of all the available information. The database lists only those oligopeptides whose chemical structures have been completely determined (directly or by translation from nucleotide sequences). It provides extensive links with the Swiss-Prot-TrEMBL peptide-protein database, as well as with the PubMed biomedical bibliographic database. EROP-Moscow also contains data on many oligopeptides that are absent from other convenient databases, and is designed for extended use in classifying new natural oligopeptides and for production of novel peptide pharmaceuticals

Low-energy general relativity with torsion: a systematic derivative expansion

We attempt to build systematically the low-energy effective Lagrangian for the Einstein--Cartan formulation of gravity theory that generally includes the torsion field. We list all invariant action terms in certain given order; some of the invariants are new. We show that in the leading order the fermion action with torsion possesses additional U(1)_L x U(1)_R gauge symmetry, with 4+4 components of the torsion (out of the general 24) playing the role of Abelian gauge bosons. The bosonic action quadratic in torsion gives masses to those gauge bosons. Integrating out torsion one obtains a point-like 4-fermion action of a general form containing vector-vector, axial-vector and axial-axial interactions. We present a quantum field-theoretic method to average the 4-fermion interaction over the fermion medium, and perform the explicit averaging for free fermions with given chemical potential and temperature. The result is different from that following from the "spin fluid" approach used previously. On the whole, we arrive to rather pessimistic conclusions on the possibility to observe effects of the torsion-induced 4-fermion interaction, although under certain circumstances it may have cosmological consequences.Comment: 33 pages, 1 figure. A new section, discussion and references added. Final (published) versio

Bifurcation structure of a swept source laser

We numerically analyze a delay differential equation model of a short-cavity semiconductor laser with an intracavity frequency swept filter and reveal a complex bifurcation structure responsible for the asymmetry of the output characteristics of this laser. We show that depending on the direction of the frequency sweep of a narrowband filter, there exist two bursting cycles determined by different parts of a continuous-wave solutions branch

Turbulent coherent structures in a long cavity semiconductor laser near the lasing threshold

We report on the formation of novel turbulent coherent structures in a long cavity semiconductor laser near the lasing threshold. Experimentally, the laser emits a series of power dropouts within a roundtrip and the number of dropouts per series depends on a set of parameters including the bias current. At fixed parameters, the drops remain dynamically stable, repeating over many roundtrips. By reconstructing the laser electric field in the case where the laser emits one dropout per round trip and simulating its dynamics using a time-delayed model, we discuss the reasons for long-term sustainability of these solutions. We suggest that the observed dropouts are closely related to the coherent structures of the cubic complex Ginzburg-Landau equation