Bifurcations and synchronization of singularly perturbed oscillators: an application case study

We present numerically obtained bifurcations of two dual singularly perturbed nonlinear oscillating circuits. Each of the circuits comprises two coupled sections: a nonlinear section with dissipation and a linear one with a small constant biasing source. The two dual oscillators show an interesting pattern of hierarchical oscillations that follow the Stern?CBrocot tree with intervals of synchronization yielding Arnold??s tongues and their corresponding devil??s-like staircases. Several numerical results are included.     

Nonlinear surface waves in arrays of curved waveguides

We study both theoretically and experimentally the nonlinear surface waves at the edge of curved waveguide arrays with a surface defect. We show that the nonlinear coupling between different linear modes supported by the array can lead to beam switching to different output waveguides with increasing of the nonlinearity strength. Our experimental observations are in good agreement with the numerical modelling.     

Spatiotemporal toroidal waves from the transverse second-harmonic generation

We study the second-harmonic generation via transversely matched interaction of two counterpropagating ultrashort pulses in chi(2) photonic structures. We show that the emitted second-harmonic wave attains the form of spatially expanding toroid with the initial thickness given by the cross correlation of the pulses. We demonstrate the formation of such toroidal waves in crystals with random ferroelectric domains as well as in annularly poled nonlinear photonic structures.     

Spiraling multivortex solitons in nonlocal nonlinear media

We demonstrate the existence of a broad class of higher-order rotating spatial solitons in nonlocal nonlinear media. We employ the generalized Hermite-Laguerre-Gaussian ansatz for constructing multivortex soliton solutions and study numerically their dynamics and stability. We discuss in detail the tripole soliton carrying two spiraling phase dislocations, or self-trapped optical vortices.     

Crystal and molecular structure of cis- and trans-2,4-dihydroxy-2,4-dimethylcyclohexanetrans-1-acetic acid γ-lactone

During the transformation process of limonene to tetrahydrofuran derivatives, the title compounds (±)-( 4 ) have been obtained as crystalline products and subjected to X-ray analysis. The crystals of trans-( 4 ) are orthorhombic, space group P2₁2₁2₁, with the lattice constants a = 7.0445(5) Å, b = 10.0908(4) Å, c = 14.0309(6) Å; the absolute configuration at atoms C1, C2, and C4 is R_c1, S_c2, and R_c4, respectively. The isomeric form cis-( 4 ) crystallizes in the monoclinic system, space group P2₁, with the following unit-cell parameters: a = 10.8275(4) Å, b = 8.6994(5) Å, c = 16.4722(6) Å, β = 106.515(3)°. The asymmetric part of the unit cell of cis-( 4 ) contains three independent molecules. Each of these three molecules has the identical absolute configuration at all centers of chirality: S_c1, S_c2, and R_c4. © John Wiley & Sons, Inc.     

Synthesis and Structural Studies of New (Triphenylphosphine)(trialkoxysilanethiolato)gold(I) Complexes

Compounds of general formula Au{SSi(OR)₃}(PPh₃), R = Prⁱ ( 1 ), Bu^s ( 2 ) or Bu^t ( 3 ), have been obtained by reaction of AuCl(PPh₃) with triethylammonium salts of respective silanethiols, (RO)₃SiSH. Molecular and crystal structures of 1 , 2 , and 3 have been determined by the single crystal X‐ray structural analysis. Compounds 1 and 2 are the first structurally characterized metal derivatives of hydrolytically unstable trialkoxysilanethiols (PrⁱO)₃SiSH and (Bu^sO)₃SiSH.     

2′-Deoxyisoguanosine and Base-Modified Analogues: Chemical and Photochemical Synthesis

The synthesis of 2′-deoxyisoguanosine ( 2 ), and the pyrrolo[2,3-d]pyrimidine and pyrazolo[3,4-d]pyrimidine 2′-deoxyribonucleosides 3 and 4 is described. Condensation of the imidazole precursor 5 with benzoyl isocyanate followed by reaction with ammonia gave 2 . Its N(7) regioisomer was obtained from 6 . Compound 2 was also prepared by the photochemically induced conversion of 2-Chloro- and 2-bromopurine 2′-deoxyribofuranosides 9a and 10 , respectively, in aqueous solution, The photo reaction was further used for the synthesis of the compounds 3 and 4 starting with the amino-chloro-2′-deoxynucleosides 9b and 9c , respectively.     

The structure of the b-completion of space-time

Structured space, as a natural generalization of the manifold concept, is defined to be a topological space with a sheaf of real function algebras which are suitably localized and closed with respect to composition with smooth Euclidean functions. Vector fields, differential forms, linear connection and curvature are introduced on structured spaces. It is shown that structured spaces correctly model space-times with singularities. Schmidt's b-boundary of space-time is constructed in the category of structured spaces, and well known difficulties with the b-boundaries of the closed Friedman and Schwarzschild space-times are disentangled. It is argued that the b-boundary of space-time, when considered in the category of structured spaces, can serve as a good definition of classical singularities.     

SITE-TO-SITE DIFFUSION IN PROTEINS AS OBSERVED BY ENERGY TRANSFER AND FREQUENCY-DOMAIN FLUOROMETRY *

Abstract We report measurements of the site-to-site diffusion coefficients in proteins and model compounds, which were measured using time-dependent energy transfer and frequency-domain fluorometry. The possibility of measuring these diffusion coefficients were shown from simulations, which demonstrate that donor (D)-to-acceptor (A) diffusion alters the donor frequency response, and that this effect is observable in the presence of a distribution of donor-to-acceptor distances. For decay times typical of tryptophan fluorescence, the simulations indicate that D-A diffusion coefficients can be measured ranging from ^?7 to ^?5 cm²/s. This possibility was verified by studies of a methylenechain linked D-A pair in solutions of varying viscosity. The D-A diffusion was also measured for two labeled peptides and two proteins, melittin and troponin I. In most cases we used global analysis of data sets obtained with varying amounts of collisional quenchers to vary the donor decay time. Unfolding of troponin I results in more rapid D-A diffusion, whereas for melittin more rapid diffusion was observed in the α-helical state but over a limited range of distances.