A remarkable theorem of Donaldson [D] says that a symplectic 4manifold admits a Lefschetz pencil by symplectic surfaces. Given a Lefschetz pencil on a 4-manifold X, one can blow up points at the base locus to get a Lefschetz fibration of X over S, which admits a nice handlebody decomposition and can be described by geometric monodromy representation into the mapping class group of a regular fib...

A mixed matrix pencil is a matrix pencil which has two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. In this paper, we characterize the indices of nilpotency of the Kronecker canonical form for a mixed matrix pencil in terms of matroids. As a byproduct, we provide an algorithm for computing t...

PURPOSE The Health Behavior in School-aged Children (HBSC) study is a cross-national survey examining health and lifestyle behaviors of adolescents, traditionally administered by paper and pencil in a school setting. The purpose of the present study was to investigate if a computer format of the questionnaire would affect the responses of the adolescents in comparison with the paper and pencil ...

Nonmonetary incentives lead to small increases in response rates to mailed questionnaires. However, inclusion of a pen or pencil, which may be a facilitating factor as well as a reward, has not been shown to improve response to health surveys in prior trials. In 2001 and 2002, the authors conducted two US trials in which a study-logo pen or pencil was randomly included in a second questionnaire...

Type Ia supernovae (SNe Ia) can be calibrated to be good standard candles at cosmological distances. However, at z > ∼ 1, gravitational lensing leads to significant level of noise in a SN Hubble diagram. We propose a pencil beam survey of SNe Ia which would yield a significant number of SNe in redshift bins of 0.1 for z up to 2. The SN number count can provide a direct probe of cosmology which ...

For cubic pencils we define the notion of an involution curve. This is a curve which intersects each pencil in exactly one non-base point pencil. Involution curves can be used to construct integrable maps plane leave invariant