Qualitative properties of the boundary derivative of the capacity potential for special classes of annular domains

Let U(p) denote the capacity potential in an annular domain Ω (bounded by Jordan curves). We describe the qualitative behavior of ∥Δ∥ on the line segments of ?Ω which are arbitrary, radial, or ν-directional (for some vector ν ≠ 0) in the respective cases where Ω is a convex, starlike, or ≠-convex annular domain. We apply these results to some free-boundary extremal problems in which the capacity plus weighted area functional is minimized in restricted classes of annular domains Ω.     

Radial sums of ridge functions: A characterization

We extend and sharpen the characterization of radial sums of ridge functions of two variables given in an earlier paper. More precisely, a bound on the degree of certain polynomials is given which depends on the angles between the ridges; not only is this bound best possible but also a converse result holds. Furthermore, variants of this characterization which hold for higher dimensional analogues are also given. These results are then applied to certain parallel am models in computed tomography to obtain more precise and otherwise improved characterizations of algorithms which commute with rigid motions.     

CČerenkov second-harmonic generation by nondiffracting Bessel beams in bulk optical crystals

A new method of optical second-harmonic generation (SHG) in bulk media is proposed, using Bessel beams which realize Cerenkov phase matching. Single-domain crystals are presently considered. For noncollinear emission the scheme has the advantage of achieving conversion efficiencies of typically about double those achieved with unfocused Gaussian beams, over the same temperature bandwidth. The harmonic radiation is analysed using a Hankel transform-based spectral method. Numerical examples are given based on the crystal KNbO3, and possible experimental arrangements are suggested for the practical implementation of this method.     

Organic field-effect transistors from solution-deposited functionalized acenes with mobilities as high as 1 cm2/V x s

We present the device parameters for organic field-effect transistors fabricated from solution-deposited films of functionalized pentacene and anthradithiophenes. These materials are easily prepared in one or two steps from commercially available starting materials and are purified by simple recrystallization. For a solution-deposited film of functionalized pentacene, hole mobility of 0.17 cm2/V.s was measured. The functionalized anthradithiophenes showed behavior strongly dependent on the substituents, with hole mobilities as high as 1.0 cm2/V.s.     

Robust, soluble pentacene ethers

We report the synthesis and characterization of a series of alkoxy-substituted silylethynylated pentacene derivatives (R = CH(2)CH(2), CHCH, CH(2)). All three compounds are easily prepared, soluble in common organic solvents, and stable both as solids and in solution. Two of the derivatives possess significant pi-face interactions in the crystal. Values for lambda(max) for these new pentacene derivatives range from 621 to 674 nm, and oxidation potentials lie between 109 and 301 mV versus ferrocene.