Variant of the geometrically nonlinear theory of anisotropic shells with allowance for transverse shear

A very simple variant of the geometrically nonlinear theory of anisotropic shells with allowance for the high compliance of the material in transverse shear is proposed. From this theory there follow, as a special case, the equations for an isotropic shell; these differ from the relations of [2] with respect to terms of the order of the ratio of the thickness of the shell to the radii of curvature small as compared with unity. The equations obtained are used to solve the problem of the stability of orthotropic shells of revolution relative to the starting axisymmetric state of stress.Translated from Mekhanika Polimerov, No. 5, pp. 863–871, September–October, 1969.     

Six-dimensional nearly Kähler manifolds of cohomogeneity one

We consider six-dimensional strict nearly Kähler manifolds acted on by a compact, cohomogeneity one automorphism group G$G$. We classify the compact manifolds of this class up to G$G$-diffeomorphisms. We also prove that the manifold has constant sectional curvature whenever the group G$G$ is simple.     

Measurement of fiber chromatic dispersion using spectral interferometry with modulation of dispersed laser pulses

We propose and experimentally demonstrate a method for fiber dispersion measurement based on the modulation of laser pulses stretched by the fiber under test. The measured spectrum of the modulated pulses is the result of the interference between the stretched pulse spectra shifted by the modulation harmonics. The interference pattern is processed as in Fourier transform spectral interferometry. Unlike to conventional spectral interferometry, environmental conditions do not affect the interferogram due to the lack of any interferometer; additionally, large dispersions can be characterized by the method proposed. Its high accuracy is demonstrated in experimental comparison with the widely used phase shift technique.     

Noise enhanced persistence in a biochemical regulatory network with feedback control

We find that discrete noise of inhibiting (signal) molecules can greatly delay the extinction of plasmids in a plasmid replication system: a prototypical biochemical regulatory network. We calculate the probability distribution of the metastable state of the plasmids and show in this example that the reaction rate equations may fail in predicting the average number of regulated molecules even when this number is large, and the time is much shorter than the mean extinction time.     

On Multiple Scattering of Radiation by an Infinite Grating of Dielectric Circular Cylinders at Oblique Incidence

A rigorous analytical representation for the multiple scattering coefficients of the fields radiated by an infinite grating of dielectric circular cylinders excited by an obliquely incident plane electromagnetic wave is derived in terms of the “well-known scattering coefficients of an isolated dielectric cylinder at oblique incidence” and “Schl?milch series”. In addition, a generalized sum-integral grating equation is acquired for the multiple scattered amplitude of a cylinder at oblique incidence in the grating in terms of the scattering coefficients of the insulating dielectric circular cylinder at oblique incidence.      

Formation and annihilation of laser light pulse quanta in a thermodynamic-like pathway

We present a theoretical and experimental study of multiple pulse formation in passively mode-locked lasers. Following a statistical-mechanics approach, the study yields a thermodynamic-like "phase diagram" with boundaries representing cascaded first order phase transitions. They correspond to abrupt creation or annihilation of pulses and a quantized rf power behavior, as system parameters (noise and/or pumping levels) are varied, in excellent accordance with the experiments. Remarkably, individual pulses carry an almost constant quantum of energy.     

The first solid-phase synthesis of bis(oxazolinyl)pyridine ligands

Chiral Pybox (pyridine-2,6-bis(oxazoline)) ligands can be cleanly and efficiently prepared on polystyrene support via a five-step solid-phase synthetic sequence. Cu(I)-complexed polymer-bound Pybox was used as a catalyst in the first heterogeneously catalyzed asymmetric addition of alkynes to imines. Best enantioselectivity was observed with (t)Bu-substituted oxazolines.     

Definitive evidence for monoanionic binding of 2,3-dihydroxybiphenyl to 2,3-dihydroxybiphenyl 1,2-dioxygenase from UV resonance Raman spectroscopy, UV/Vis absorption spectroscopy, and crystallography

Ultraviolet resonance Raman spectroscopy (UVRRS), electronic absorption spectroscopy, and X-ray crystallography were used to probe the nature of the binding of 2,3-dihydroxybiphenyl (DHB) to the extradiol ring-cleavage enzyme, 2,3-dihydroxybiphenyl 1,2-dioxygenase (DHBD; EC 1.13.11.39). The lowest lying transitions in the electronic absorption spectrum of DHBD-bound DHB occurred at 299 nm, compared to 305 nm for the monoanionic DHB species in buffer. In contrast, the corresponding transitions in neutral and dianionic DHB occurred at 283 and 348 nm, respectively, indicating that DHBD-bound DHB is monoanionic. These binding-induced spectral changes, and the use of custom-designed optical fiber probes, facilitated UVRR experiments. The strongest feature of the UVRR spectrum of DHB was a Y8a-like mode around 1600 cm(-1), whose position depended strongly on the protonation state of the DHB. In the spectrum of the DHBD-bound species, this feature occurred at 1603 cm(-1), as observed in the spectrum of monoanionic DHB. Raman band shifts were observed in deuterated solvent, ruling out dianionic binding of the substrate. Thus, the electronic absorption and UVRRS data demonstrate that DHBD binds its catecholic substrate as a monoanion, definitively establishing this feature of the proposed mechanism of extradiol dioxygenases. This conclusion is supported by a crystal structure of the DHBD:DHB complex at 2.0 A resolution, which suggests that the substrate's 2-hydroxyl substituent, and not the 3-hydroxyl group, deprotonates upon binding. The structural data also show that the aromatic rings of the enzyme-bound DHB are essentially orthogonal to each other. Thus, the 6 nm blue shift of the transition for bound DHB relative to the monoanion in solution could indicate a conformational change upon binding. Catalytic roles of active site residues are proposed based on the structural data and previously proposed mechanistic schemes.     

Unified approach to short optical pulse recording and spatial imaging with subwavelength resolution

We propose and numerically demonstrate a simple method for measuring waveforms of optical pulses that have spectral bandwidths much larger than the passband of the measuring system, thus enabling a kind of temporal superresolution. The technique is based on pulse intensity modulation that contains high-order harmonics. Parts of the pulse intensity spectrum that are shifted as a result of the modulation, are moved over (“umklapped”) to the center of the passband, transmitted and then recorded by an oscilloscope. The pulse intensity spectrum is restored by parts from the Fourier transform of a few oscillograms, measured after performing the temporal shifts between the pulse train and the modulation. A similar approach is applied for achieving subwavelength spatial resolution in far -field microscopy. The spatial modulation is performed by a diffraction grating. The method allows one to restore a subwavelength object in a single measurement.     

A Uniqueness Theorem of Fourier Jacobi Models for Representations of Sp(4)

It is shown that every irreducible admissible representationof Sp₄(F), where F is a p-adic field, has at most one FourierJacobi model for given Fourier Jacobi data.