Short cycles in repeated exponentiation modulo a prime

Given a prime p, we consider the dynamical system generated by repeated exponentiations modulo p, that is, by the map \({u \mapsto f_g(u)}\), where f _g (u) ≡ g ^u (mod p) and 0 ≤ f _g (u) ≤ p ? 1. This map is in particular used in a number of constructions of cryptographically secure pseudorandom generators. We obtain nontrivial upper bounds on the number of fixed points and short cycles in the above dynamical system.     

Fast oxy-cope rearrangements of bis-alkynes: competition with central C-C bond fragmentation and incorporation in tunable cascades diverging from a common bis-allenic intermediate

Fast anionic oxy-Cope rearrangements of 1,5-hexadiyn-3,4-olates can be incorporated into cascade transformations which rapidly assemble densely functionalized cyclobutenes or cyclopentenones via a common bis-allenic intermediate. The competition between fragmentation, 4π-electrocyclic closure, and aldol condensation can be efficiently controlled by the nature of the acetylenic substituents. The rearrangement of bis-alkynes with two hydroxyl substituents opens a conceptually interesting entry in the chemistry of ε-dicarbonyl compounds and suggests a new approach to analogues of rocaglamide/aglafolin.     

Photoisomerization and photochemistry of matrix-isolated 3-furaldehyde

3-Furaldehyde (3FA) was isolated in an argon matrix at 12 K and studied using FTIR spectroscopy and quantum chemistry. The molecule has two conformers, with trans and cis orientation of the O=C-C=C dihedral angle. At the B3LYP/6-311++G(d,p) level of theory, the trans form was computed to be ca. 4 kJ mol(-1) more stable than the cis form. The relative stability of the two conformers was explained using the natural bond orbital (NBO) method. In fair agreement with their calculated relative energies and the high barrier of rotamerization (ca. 34 kJ mol(-1) from trans to cis), the trans and cis conformers were trapped in an argon matrix from the compound room temperature gas phase in proportion ~7:1. The experimentally observed vibrational signatures of the two forms are in a good agreement with the theoretically calculated spectra. Broad-band UV-irradiation (λ > 234 nm) of the matrix-isolated compound resulted in partial trans → cis isomerization, which ended at a photostationary state with the trans/cis ratio being ca. 1.85:1. This result was interpreted based on results of time-dependent DFT calculations. Irradiation at higher energies (λ > 200 nm) led to decarbonylation of the compound, yielding furan, cyclopropene-3-carbaldehyde, and two C(3)H(4) isomers: cyclopropene and propadiene.     

Materials for fluorescence resonance energy transfer analysis: beyond traditional donor-acceptor combinations

The use of F?rster or fluorescence resonance energy transfer (FRET) as a spectroscopic technique has been in practice for over 50 years. A search of ISI Web of Science with just the acronym "FRET" returns more than 2300 citations from various areas such as structural elucidation of biological molecules and their interactions, in vitro assays, in vivo monitoring in cellular research, nucleic acid analysis, signal transduction, light harvesting and metallic nanomaterials. The advent of new classes of fluorophores including nanocrystals, nanoparticles, polymers, and genetically encoded proteins, in conjunction with ever more sophisticated equipment, has been vital in this development. This review gives a critical overview of the major classes of fluorophore materials that may act as donor, acceptor, or both in a FRET configuration. We focus in particular on the benefits and limitations of these materials and their combinations, as well as the available methods of bioconjugation.     

Aspherical manifolds with relatively hyperbolic fundamental groups

We show that the aspherical manifolds produced via the relative strict hyperboli- zation of polyhedra enjoy many group-theoretic and topological properties of open finite volume negatively pinched manifolds, including relative hyperbolicity, nonvanishing of simplicial volume, co-Hopf property, finiteness of outer automorphism group, absence of splitting over elementary subgroups, and acylindricity. In fact, some of these properties hold for any compact aspherical manifold with incompressible aspherical boundary components, provided the fundamental group is hyperbolic relative to fundamental groups of boundary components. We also show that no manifold obtained via the relative strict hyperbolization can be embedded into a compact Kähler manifold of the same dimension, except when the dimension is two.     

Experimental and theoretical study of self-phase modulation in sbs compression of high-power laser pulses

We study experimentally the behavior of the spectrum shape and Stokes frequency shift of stimulated Brillouin scattering (SRS)-compressed radiation within a broad range of incident-laser-pulse intensities from the threshold up to eight times the threshold values. We show that, at pulse compression of reflected radiation to subnanosecond durations (smaller than inverse spontaneous line widths), its spectrum monotonously shifts with increase in the exciting light intensity such that its Stokes shift decreases. At intensities increasing four times the threshold, the spectrum splits and acquires a twohumped shape, which is explained by the phase modulation near the SBS resonance. We construct an analytical model of self-phase modulation in SBS compression, describing the spectral splitting and chirping formation.     

Theory of high-power mode-locked lasers with a slow absorber

We develop an analytical theory of high-power passively mode-locked lasers with a slow absorber; the theory is valid at pulse energies well exceeding the saturation energy. We analyze the Haus modelocking master equation in the pulse-energy-domain representation, approximating the intensity profile function by a series in the vicinity of its peak value. We consider the high-power operation regime of subpicosecond blue–violet GaN mode-locked diode lasers, using the approach developed.     

A unilateral magnet with an extended constant magnetic field gradient

Unilateral magnetic resonance (UMR) has become, in different research areas, a powerful tool to interrogate samples of arbitrary size. Numerous designs have been suggested in the literature to produce the desired magnetic field distributions, including designs which feature constant magnetic field gradients suitable for diffusion and profiling experiments. This work presents a new approach which features extended constant magnetic field gradients with a three magnet array. Constant gradients of more than 3cm extent can be achieved in a very simple, compact and safe design. Diffusion measurements from different positions over the magnet are presented in addition to practical applications for reservoir core plug characterization. The idea of a solenoid as a probe for specific measurements in UMR is introduced. Simple profiling experiments are also presented.     

The Spatial-Temporal Lamellar Structures in the Confined Ideal Polymer Blends

We consider the formation of self-organized spatial-temporal oscillating structures in symmetric binary polymer blends confined by two flat walls. An influence of these walls on the formation of the oscillating volume structures is studied. This phenomenon is simulated by an initial boundary-value problem for the conserved order parameter (or the concentration of one of the components in a binary mixture). Under a special choice the dynamical Puri-Binder’s boundary conditions these structures look like the lamellar structures. The behavior of the order parameter is described by the modified Cahn-Hilliard equation which models so-called the non-Fickian diffusion in the symmetric binary polymer blends. The nonlinear dynamical boundary conditions correspond to the process of adsorption-desorption on the walls. As a result, these nonlinear surface processes induce into the volume the spatial-temporal asymptotically periodic structures of relaxation, pre-turbulent or turbulent type with finite, countable or non-countable points of discontinuities on the period correspondingly. The frequency of oscillations on the period follows a power-law for the relaxation type and increases exponentially in the other cases.