Influence of layer and anisotropic fluctuations of the refractive index on the beyond-the-horizon SHF propagation in the troposphere over the sea when there is an evaporation duct

On the basis of the invariant imbedding method the disturbance theory for complex constants of propagation is proposed. This approach allows us to consider the influence of layer and anisotropic fluctuations of refractive index on the beyond-the-horizon propagation in the adiabatic approximation with the existence of an evaporation duct. Finally, the authors consider some examples of the calculations and investigate stochastic effects connected with the interaction between fluctuating and regular waveguides.     

Linear optical switching in a FLC/waveguide composite device

A fast electrooptic modulation in a polymer waveguide using a ferroelectric liquid crystal has been proposed. In this device, the surface stabilized ferroelectric liquid crystal and the soft mode ferroelectric liquid crystal are used as an active material on the passive polymer waveguide, and electrooptic switching is realized by controlling the total reflection at the polymer waveguide-liquid crystal interface. The response time is of the order of several microseconds. The analogue electrooptic modulation in the waveguide is realized using the field induced linear molecular tilt of the electroclinic effect in the soft mode ferroelectric liquid crystal.     

Characteristic values of the integral equation satisfied by the Mathieu functions and its application to a system with chirality-pair interaction on a one-dimensional lattice

We investigate low-temperature behaviors of a system with chirality-pair interaction on a one-dimensional lattice. In the course of the investigation, we evaluate asymptotic forms of the characteristic values of the integral equation satisfied by the Mathieu functions. It turns out that the low-temperature behavior of correlation length of the chirality-pair correlation function is different from the one for the Ising model of spin ±1 but akin to the one for the Ising model of infinite spin.     

Synthesis of 1-(3-alkyl-2,3-dideoxy-D-pentofuranosyl)uracils with potential anti-HIV activity.

1-(3-Alkyl-2,3-dideoxy-alpha,beta-D-erythro-pentofuranosyl)uracils and 1-(3-alkyl-2,3-dideoxy-alpha,beta-D-threo-pentofuranosyl)uracils have been prepared from (E)-4,5-di-O-acetyl-2,3-dideoxy-aldehydo-D-glycero-pent-2-enose by a Michael addition reaction of the appropriate organocopper reagent followed in subsequent order by glycosidation of the resulting 3-alkyl-4,5-diacetoxypentanal with methanolic hydrogen chloride, protection with p-methoxybenzoyl chloride, and trimethylsilyl triflate catalyzed coupling with 2,4-di-O-(trimethylsilyl)uracil. The nucleosides were deprotected by treatment with 33% methylamine in absolute ethanol and separated by reversed-phase HPLC.     

Solution of the hyperbolic mild‐slope equation using the finite volume method

A finite volume solver for the 2D depth‐integrated harmonic hyperbolic formulation of the mild‐slope equation for wave propagation is presented and discussed. The solver is implemented on unstructured triangular meshes and the solution methodology is based upon a Godunov‐type second‐order finite volume scheme, whereby the numerical fluxes are computed using Roe's flux function. The eigensystem of the mild‐slope equations is derived and used for the construction of Roe's matrix. A formulation that updates the unknown variables in time implicitly is presented, which produces a more accurate and reliable scheme than hitherto available. Boundary conditions for different types of boundaries are also derived. The agreement of the computed results with analytical results for a range of wave propagation/transformation problems is very good, and the model is found to be virtually paraxiality‐free. Copyright © 2003 John Wiley & Sons, Ltd.     

The exponential characteristic of the Volterra integral operator with kernel depending on 2<Emphasis Type="Italic">N</Emphasis> variables

Exponential growth is estimated for integral operators with continuous periodic kernels of exponential type. The result is applied to the boundary-value problem for a general hyperbolic differential equation having periodic coefficients with Goursat boundary conditions. It is proved that the exponential characteristic for such a boundary-value problem has canonical form. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 38, Suzdal Conference-2004, Part 3, 2006.     

Slow cyclotron instability in a high-power backward-wave oscillator

The linear dispersion relation of a backward-wave oscillator (BWO), derived earlier by the authors, is modified to include effects of RF surface current at the beam-vacuum interface. This modified dispersion relation results in an unstable interaction between the slow cyclotron mode (SCM) and the structure mode in addition to the conventional Cherenkov instability caused by the slow space charge mode. Numerical analysis is then carried out using parameters of a BWO experiment at University of Maryland. Fine structure of the SCM instability is elucidated. The analysis indicates that BWO radiation would not be suppressed near cyclotron absorption in an infinitely long system.