Bounds on Malapportionment

Uniformly sized constituencies give voters similar influence on election outcomes. When constituencies are set up, seats are allocated to the administrative units, such as states or counties, using apportionment methods. According to the impossibility result of Balinski and Young, none of the methods satisfying basic monotonicity properties assign a rounded proportional number of seats (the Hare-quota). We study the malapportionment of constituencies and provide a simple bound as a function of the house size for an important class of divisor methods, a popular, monotonic family of techniques.     

On a conjecture of Cox and Katz

This note shows that a certain toric quotient of the quintic Calabi-Yau threefold in provides a counterexample to a recent conjecture of Cox and Katz concerning nef cones of toric hypersurfaces. Received: 8 February 2001; in final form: 17 September 2001 / Published online: 1 February 2002     

Low-density close-closed loop burst error detecting codes

In this paper, we study cyclic codes detecting a subclass of close-closed loop bursts viz. low-density close-closed loop bursts. A sub-class of CT close-closed loop bursts called CT low-density close-closed loop bursts is also studied.     

Notes on Interpolation. X (Two Boundary Value Problems)

In this paper we use (0, 2) interpolational polynomials to give an approximate solution of the differential equation y(x) + A(x)y(x) = F(x), x I := [-1, 1] j in case when the boundary values are y(-1) = and y(1) = , , R.     

Large deviation theory for a homogenized and “corrected” elliptic ODE

We study a one-dimensional elliptic problem with highly oscillatory random diffusion coefficient. We derive a homogenized solution and a so-called Gaussian corrector. We also prove a “pointwise” large deviation principle (LDP) for the full solution and approximate this LDP with a more tractable form. Applications to uncertainty quantification are considered.     

Pulse compression of nanojoule pulses in the visible using microstructure optical fiber and dispersion compensation

Experimental results on the pulse compression of 1-nJ, 150-fs pulses from a tunable, 76-MHz Ti:sapphire laser oscillator operating at around 750 nm are reported. The length of the pulses can be compressed to nearly one tenth by applying a high-delta, single-mode microstructured optical fiber exhibiting zero group-delay dispersion at 767 nm, and by a prism-pair/chirped-mirror compressor. The experimental results are verified by theoretical investigations modeling the pulse propagation taking into account non-linear self-phase modulation and fiber dispersion. Received: 10 June 2002 / Revised version: 15 November 2002 / Published online: 12 February 2003 RID="*" ID="*"Corresponding author. Fax: +36-1/375-4553, E-mail: szipoecs@sunserv.kfki.hu     

Radiative Transport in a Periodic Structure

We derive radiative transport equations for solutions of a Schrödinger equation in a periodic structure with small random inhomogeneities. We use systematically the Wigner transform and the Bloch wave expansion. The streaming part of the radiative transport equations is determined entirely by the Bloch spectrum, and the scattering part by the random fluctuations.     

Ultrasonics in heterogeneous metal catalysis: sonochemical chemo- and enantioselective hydrogenations over supported platinum catalysts

Sonochemical chemo- and enantioselective hydrogenations over supported platinum catalysts are described. We disclose our results with respect to a sonochemical modification of the chemoselective hydrogenation of cinnamaldehyde over supported platinum catalysts, and the asymmetric hydrogenation of ethyl pyruvate promoted by various ultrasonic pretreatments. The ultrasonic pretreatment of the supported platinum catalysts was found to be highly beneficial in almost every case, improving both the catalytic activity and selectivity. The effect of additional experimental variables, such as hydrogen pressure, catalyst support, temperature and the ultrasonic insonation time were also studied. The enantioselectivity of the hydrogenation of ethyl pyruvate increased up to 97.1% ee. In the case of cinnamaldehyde hydrogenation, the selective preparation of cinnamyl alcohol became possible. The theoretical aspects of the working mechanisms in comparison with 'silent' reactions will also be provided.     

Theory of the sticking coefficient for atom-surface scattering

A calculation of the sticking coefficient is presented for a one-dimensional system with harmonic interactions. The physical basis for the results is discussed and it is shown how general conclusions may be drawn for three-dimensional systems.