Counting Horoballs and Rational Geodesics

Let M be a geometrically finite pinched negatively curved Riemannianmanifold with at least one cusp. The asymptotics of the numberof geodesics in M starting from and returning to a given cusp,and of the number of horoballs at parabolic fixed points inthe universal cover of M, are studied in this paper. The caseof SL(2, Z), and of Bianchi groups, is developed. 2000 MathematicsSubject Classification 53C22, 11J06, 30F40, 11J70.     

Mid-infrared intersubband emission from optically pumped asymmetric coupled quantum wells

Mid-infrared optical emission due to intersubband transitions between excited conduction subbands of a coupled quantum well structure is studied. The emission process is based on optical pumping of free carriers from the ground subband into the third subband followed by a radiative transition from the third subband into the second subband and a fast phonon assisted relaxation into the ground subband. We have observed spontaneous emission at 14 μm that persists up to room temperature. Our results indicate that population inversion between conduction subbands and large stimulated gain can be achieved.     

Intersubband photocurrent from double barrier resonant tunneling structures

Simple models of semiconductor-based double barrier resonant tunneling structures predict a large accumulation of charge carriers in the structure. These carriers can be excited optically from one subband to another generating photocurrent. In this work we have investigated the photo-induced current due to intersubband excitation in double barrier structures. We have found that the origin of the photocurrent is accumulation of quantized carriers in the emitter-barrier junction of the structure, rather than accumulation of carriers in the double barrier quantum well. This photon assisted tunneling process in double barrier structures may be used for infrared detection.     

Diophantine approximation for negatively curved manifolds

Let M be a geometrically finite pinched negatively curved Riemannian manifold with at least one cusp. Inspired by the theory of Diophantine approximation of a real (or complex) number by rational ones, we develop a theory of approximation of geodesic lines starting from a given cusp by ones returning to it. We define a new invariant for M, theHurwitz constant of M. It measures how well all geodesic lines starting from the cusp are approximated by ones returning to it. In the case of constant curvature, we express the Hurwitz constant in terms of lengths of closed geodesics and their depths outside the cusp neighborhood. Using the cut locus of the cusp, we define an explicit approximation sequence for a geodesic line starting from the cusp and explore its properties. We prove that the modular once-punctured hyperbolic torus has the minimum Hurwitz constant in its moduli space. Received: 24 October 2000; in final form: 10 November 2001 / Published online: 17 June 2002     

Boundary value problems on planar graphs and flat surfaces with integer cone singularities, II: The mixed Dirichlet-Neumann problem

In this paper we continue the study started in Hersonsky (in press) [16]. We consider a planar, bounded, m-connected region Ω, and let ∂Ω be its boundary. Let T be a cellular decomposition of Ω∪∂Ω, where each 2-cell is either a triangle or a quadrilateral. From these data and a conductance function we construct a canonical pair (S,f) where S is a special type of a (possibly immersed) genus (m−1)singular flat surface, tiled by rectangles and f is an energy preserving mapping from T(1) onto S. In Hersonsky (in press) [16] the solution of a Dirichlet problem defined on T(0) was utilized, in this paper we employ the solution of a mixed Dirichlet-Neumann problem.     

Acetylcholine detection at micromolar concentrations with the use of an artificial receptor-based fluorescence switch

An inclusion complex between water-soluble p-sulfocalix[n]arene (Cn, n=4, 6, 8) and the chromophore trans-4-[4-(dimethylamino)styryl]-1-methylpyridinium-p-toluenesulfonate (D) formed the basis for a highly sensitive sensor for the selective detection of neurotransmitter acetylcholine (ACh). Formation of the [Cn.D] complex (Ka=approximately 10(5) M(-1)) was accompanied by a drastic increase (up to 20-60-fold) in the chromophore relative quantum yield and by a large hypsochromic shift of the emission band maximum. The observed optical effects are fully reversible: ACh displaces the chromophore molecules from the calixarene cavity as shown by the reappearance of the free chromophore emission band. Formation and dissociation of the complex were studied by fluorescence, 1H NMR, and UV-vis absorption spectroscopies. The [Cn.D] complex is capable of sensing ACh selectively in solution at sub-micromolar concentrations. Immobilization of monocarboxyl p-sulfocalix[4]arene (C4m) on an oxide-containing silicon surface is in keeping with its properties, such as chromophore binding and the ability of the immobilized inclusion complex to detect ACh. The unique [Cn.D] complex optical switching paves the way for application in ACh imaging and optoelectronic sensing.